So the base case is n = 7. You need to show that

3^7 < 7!

Then consider that whenever you increase n by 1, you multiply the left side by 3, and the right side by a number greater than 3. Thus the right side will continue to be greater than the left side. This is what you will write formally as the induction step. (Assume 3^n < n!. Then show that 3^(n+1) < (n+1)! is true.)