Is there a way to tell if a quiet guy likes you when doing things together.

What exactly is your relationship with this guy?
If you just met or are getting to know each other, then this guy might just not be sure if he wants to do things together with you again. Also how long have you not been receiving emails?
If your relationship with him is good or you know each other well, then maybe he's possibly trying to figure out how he feels about you, or even how you feel about him.
He also might just be busy, for both situations. Or he's just deciding for a long time.
Anyways, see if he's ever acting nervous or weird around you, or he cares about your opinions.

The fact that a person is quiet doesn't reveal anything in particular about his thinking or his personality. The thinking of an angry person who is quiet is going to be different than the thinking of a sad person who is quiet. In general, trying to deduce what other people are thinking is a mug's game. You might only have limited success when engaging a quiet person in conversation but you'll have a better idea of how they think than if you just try to figure it out by yourself. Communication is a two-way street.

How long has it been since he was in touch with you?

I think I am just in an email relationship with the guy. I mean that I am just getting to know the person better before doing things with him. The guy did say in the email that I am the type of girl he likes. I am just not sure what he is thinking. Can I have some advice on what to do about this. Thanks.

He has been doing emails with me for a few weeks already.

That wasn't her question.

Maybe he's just shy to tell you anything.
If you want to know what he's thinking, maybe send him email and ask him, how you would like, if he wants to do something with you again. Something relating to that. You won't know unless you ask him.
Don't feel uncomfortable.
Just do it.