She enjoy eating at two type of restaurants; italian and mexican.

There are a few errors in this sentence.

Here is what it should look like:

She enjoys eating at two types of restaurants, Italian and Mexican.

- the verb enjoy must agree with the subject she

-type must be plural because you are talking about two restaurants in your sentences

- I believe a comma should follow restaurants because there needs to be a pause.

You don't use a semicolon in this case because you are not connecting an independent clause. Independent clauses can stand alone meaning it is a complete thought/complete sentence. In your case Italian and Mexican cannot do cannot stand alone.

**Not only are semicolons used to connect independent clauses they are also used connect a thought meaning if the first part of the sentence is an independent clause but the second part isn't and it continues on talking about the first part of the sentence then you would put a semicolon between the two. For example: Love isn't something you experience; it's something you chose to do even when it is hard to do. (I made this sentence up).

Hopefully this helps and good luck.