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a. I don't think I can do anything you want.
Can't this sentence mean two things?
a1. I think I can't do anything you want.
a2. I don't think I can't do just anything you want.
b. You're mistaken to think you can do anything I want.
Can't this sentence mean two things?
b1. You're mistaken to think you can do even one of the things I want.
b2. You're mistaken to think you can do just anything I want.
In written and normal spoken English, A1 and B1 are how people will interpret this unless the context is very specific.
When you say "just anything" I'm interpreting it to mean "absolutely anything." That being the case, it is possible for both A2 and B2 to be the case. However, the spoken inflection would need to be strong as would the context. In written English, there would likely be a clue in the punctuation or formatting. For example,
Mike: This is amazing work. It seems you can do anything I want.
Sally: Well, I can't do anything you want.
I've purposely chosen two different genders, because there is a possible humorous innuendo here. If they were the same gender, it could also be a humorous allusion to not being able to move mountains or something.
