These two mountains of brass are the backdrops of the scene of which the four chariots ‘come out’ from. The chariots themselves I take the arguably most commonly held view: the four winds represents angels directing the four monarchies that overturned the known world starting with the Babylonian, Persian, Greek and then the Roman empire. The question before us then is what are these brass mountains, why two and how related to the chariots?
First as to the basic meaning we can take a step more certain. Most commentaries will all agree that we have represented in the brass mountain a sense of immovable, unstoppable strength covering a wide base. For example one author says:
Mountains are the Bible emblems of immoveable steadfastness; and mountains of brass is just a strengthening of the emblem (Lectures on the Prophecies of Zechariah, by Ralph Wardlaw, p130)
However, is this immovable sovereignty of God in general upon which these kingdoms rise and fall, or the immovable power of the kingdoms themselves, or something else? Also, why two mountains? Are we to take significance in the number two, or are we to assume this represents just a narrow passageway between one unmovable will of God whereby his decrees can slip through from his narrow opening for the event?
To take a cautious step forward in what is not clear at all, it seems the only way forward is to stick close to the chariots, otherwise any imaginative idea may be proposed. The solution must compliment the prophecy regarding the four monarchies. If we imagine it ourselves I think the answer will appear to us as obvious. If we looked upon brass-mountains through which chariots rode between their narrow openings, we would have two obvious impressions. One, the chariots are actually very small compared to the mountains. Two, the mountains keep everything else out from the scene except these chariots that they let pass. Therefore these mountains can’t directly speak to the power of the chariots themselves, but rather to the power of God’s will in allowing them to pass and esnuring they alone do pass.
Regarding the meaning of two, there are two positions that seem reasonable to me. (One my own conjecture, but I think a well received one if I may.) First, 'two' may mean nothing really other than a way to describe a mountain range with an opening for God’s sovereign will. Second (my proposed possibility) is that if we regard the immovable mountains as not only allowing passage but from their holy establishment but in regard to their high peaks viewing the seen are thereby acting as witnesses of the truthfulness of the prediction, then there is a plain meaning in the number two before is. For it is not biblical to accept the testimony of a witness unless there be at least two witnesses in establishing the truth of a matter (Deuteronomy 17:6). If we take this position then, the two brass-mountains are two reliable witnesses of God’s all powerful and unstoppable will. These emblems make the four kingdoms themselves, though tiny in comparison, unstoppable in their over-turnings of the world according to the foreordained purposes of God under the management of his angels.
However this really does not provide proper confidence to a good interpretation unless we can somewhere find mountains as taking the role of a witness in the Bible. As we look for such an indication it is no surprise that scripture has used this allusion to the high view of a fixed mountain to the concept of a testimony before:
Hear what the LORD says: Arise, plead your case before the mountains, and let the hills hear your voice. Hear, you mountains, the indictment of the LORD, and you enduring foundations of the earth, for the LORD has an indictment against his people, and he will contend with Israel.( The Holy Bible: English Standard Version. 2001 (Mic 6:1–2). Wheaton: Standard Bible Society.)
So there we have it.