In this example:

I don't think I'll be able to make it.

Notice that the speaker says "I don't think I'll be able to" instead of "I think I wonn't be able to". In English, it's better to make "do" negative and keep the modal ("can", "will", "should", etc.) positive:

I don't think I should leave him here by himself.

I don't think I've been there.

I don't think she wants to go.