～てもいい

Noun, い-Adjective, or な-Adjective + てもいい is a construction in Japanese that is used to express that something is 'okay', or 'alright'. It is also frequently used as a question to ask if you 'can', or 'may' do something.

• 電車(でんしゃ)でもいい。
  I am fine even if it is by train. (It does not need to be by car)
• お茶(ちゃ)冷(つめ)たくてもいい？
  Is it okay even if the tea is cold? (Would you prefer I heat it?)
• 肉(にく)が好(す)きでもいい。
  It is okay even if you like meat. (I won't force you to eat something vegetarian)

As can be seen, with い-Adjectives, we will need to use the conjugation form. This is created by removing the い and then replacing it with く.
This phrase is also regularly used without the も, but is considered a bit more direct/casual in those cases. It is best to remove the も only when talking to people that you know well.
てもいい is an expression that literally means て (noun, etc) も (also) いい (is good).
Similarly to the てもいい grammar point that is used with verbs, this variant may also be used as a question. To do this, you simply need to follow てもいい with ですか, or the more casual の.

• 焼(や)きそばでもいいですか？
  Is it okay even if it is yakisoba?
• これ食(た)べてもいいの？
  Is it okay if we eat this? (Is this one that is okay to eat?)