In 2 Chronicles we read:
... Solomon had 4,000 stalls for horses and chariots and 12,000 horsemen ...- 2 Chronicles 9:25
... but in 1 Kings:
Solomon had 40,000 stalls of horses for his chariots, and 12,000 horsemen. - 1 Kings 4:26
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Answering how many there actually were isn't going to be possible here because there is a definite conflict between the verses, and the honest answer is "nobody's sure". And opinion answers don't count here. Since your question is a valid one asked quite often, I hope you'll indulge me and let me answer something slightly different that still gets at the heart of your question.
A fair and on-topic question would be "How do Apologists address/resolve this discrepancy?" I'd like to answer that, since it is answerable. If that's not what you're looking for, and you really want an answer to how many horses there are, the answer is "we're not sure" and you can stop reading there. If you want to know how we can read those verses and not scream "The Bible isn't inerrant!!!" read on.
As covered in Rules behind resolving alleged Biblical discrepancies the field of Apologetics hinges on avoidance of logical fallacies in explanations, and sticks to standard Christian doctrines including Biblical inerrancy, infallibility, and inspiration.
Most Apologetics experts that I'm aware of subscribe to the definition of inerrancy covered at From a Fundamentalist standpoint, what does the phrase “Inspired, infallible, inerrant Word of God” mean? This is important to define, in order to avoid straw-man arguments. Short version: The original manuscripts are believed to be inerrant, not the translations. Many translations have had known errors. copyist errors are well-documented and expected. Yet, for doctrinal purposes, we have enough manuscripts to know that there aren't any critical doctrinal issues affected by such errors.
With that out of the way, one answer is already obvious. This could easily be a copyist error. That's acceptable within the bounds outlined above. The number of horses certainly doesn't affect central doctrines.
The second possibility is that these are two different counts. Solomon certainly gained enormous wealth during his reign. The number of horses and horsemen certainly grew, so it it possible that one cont is from early in his reign and another is later in his reign.
Personally, I subscribe to the copyist error, but either way, this discrepancy doesn't pose a problem, either for the doctrine of inerrancy, nor does it have any other theological importance.
I did some searching, and a very similar error can be found at CARM:
There are two possible explanations for this discrepancy. 1) A copyist error. 2) The difference is due to time; that is, one account is at the beginning of Solomon's reign (1 Kings 4:26), and the other at the end (2 Chron. 9:25). I believe the most probable is a copyist error since we can see that Chronicles does have copyist errors in other areas. Therefore, it is probable that the same thing occurred here.
One number was taken at the beginning of his reign, the other at the end. This is at least plausible, even if it is not a very satisfying explanation.
These two accounts were not written by the same person. It is possible that what the respective authors considered a "stall" was functionally different ("stalls for horses" vs. "stalls for horses and chariots"). (Reference)
Another variation of this argument focuses on 2 Chr 9:25b, "whom he bestowed in the chariot cities, and with the king at Jerusalem." (The translation is important to this point.) The thesis is that these are two different types of counting, one being a more inclusive total than the other.
This is very unpopular in certain circles, but some theorize that this minor discrepancy is an error made by someone copying the text. These people (here's one example) do not necessarily discredit the Bible or say that it is unreliable.
I have read, although I do not know Hebrew and cannot verify, the following is accurate: the difference between 40,000 and 4,000 could be as simple as the little dot above the Hebrew character that represents a zero. With the agent handling of manuscripts perhaps one dot became worn out or illegible. Or as has been previously noted, a copyist error of one small dot.
In 1 Kings 10:26 Solomon had 1,400 chariots and 12,000 horses. He stationed some of them in the chariot cities and some near Jerusalem: Solomon built up a huge force of chariots and horses. This statement is after the 40,000 stated in 1 kings 4:26. Notice the number of horsemen never changes from 12,000 horses or horsemen from 1 Kings 4:26 , 2 Chron. 9:25 and 1 kings 10:26. Solomon housed those in the 4000 stalls across the land. So throw out the speaking on different time & on different things. Even if one stall per horse and chariot. It only equals 13,400 stalls. This makes the case that 20,000 is in excess, 40,000 is not even in the picture. In addition, Deuteronomy 17:16 " But he shall not multiply horses to himself, nor cause the people to return to Egypt, to ..... multiply horses:" All translations have documented errors in them. I conclude the one time statement of 40,000 stall is an (kJV) error. Also the Battle of Kadesh (Kadesh inscriptions) is stated to have been the largest chariot battle ever fought, involving between 5,000 and 6,000 chariots in total in light of another (kjv) misprint; 1 SAMUEL 13:5 THE PHILISTINES ARMY OF 30,000 CHARIOTS, which should be three thousand" as stated in the Arabic and Syriac versions and would be the largest chariot army in the scriptures. So as for 30,000 to 6000 chariots, never have any people in the history of the world, are known to have so many chariots of war (Gill's Exposition 1 SAM 13:5).