According to Exodus 34, Moses went up Mount Sinai two times to receive the covenant tablets.
The first ascent is associated with the original tablets. Moses later descends, sees the Israelites worshiping the golden calf, and breaks those tablets. After the covenant is renewed, Exodus 34 tells Moses to cut two replacement tablets and go up Mount Sinai again. God writes the words of the covenant on the second set.
The chapter also describes Moses staying on the mountain for forty days and forty nights during this second period, without eating bread or drinking water. When he comes down, his face shines because he has spoken with God, so he wears a veil before the Israelites.
The two ascents should not be confused with the forty-day duration of a stay. Nor should the number be merged with other mountain appearances in Exodus, since the question concerns receiving the covenant tablets specifically.