(((3!)!) - (((3!)!) / (3!))) / (3!)
= (720 - (720/6)) / 6
= (720 - 120) / 6
= 600 / 6
= 100
Some of the parentheses are not necessary if you assume standard precedence rules but I put them in to avoid possible ambiguity.
Here's what it would look like with standard precedence rules applied. It's more readable.
((3!)! - (3!)! / 3!) / 3!