The Gemara tells us that we know the Luchot, containing the Ten Commandments, were broken on this day by means of a simple mathematical calculation. Although there is disagreement as to when the Ten Commandments were given to the nation of Yisrael, all agree that Moshe went up to Mount Sinai to get the Luchot on the seventh day of the month of Sivan.
As proof of this, the Gemara brings the verse in Shemot 24:16 which says that Moshe "was called (to the mountain) on the seventh day."
We also know from a verse (Shemot 24: 18) that Moshe "was on the mountain for 40 days and 40 nights." As Sivan that year was 30 days long, Moshe was on the mountain for 24 days in Sivan, and the first 16 days of the next month, Tammuz.
On the seventeenth day of Tammuz, Moshe descended from the mountain. Seeing what the nation was doing with the Golden Calf, he broke the Luchot. (Torah.org)
[Since the 17th of Tammuz fell on Shabbat, the fast was postponed until today, Sunday July 24th.]
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