Can someone please illustrate me what does the word "only" mean in terms of math? I mean lets assume someone told me

"only motorcycles can enter this gate" so what should I understand from this? I'm really new on logic and frankly I'm not good as much as in math so please take that into consideration and I know all person has its own ability of understanding/learning.

This is as much English as math. You have to think about what logical statement has the same meaning.

You will be writing something like "If _____, then _____". What has to go in each blank in order to mean "Only motorcycles can enter this gate"?

If this is a problem you were assigned, it may be helpful to look at answers given to similar examples or exercises, to see what form is expected; please show them to us, so we can be sure we are leading you in the right direction!