The box can contain no more.

The correct answer is C. No more can be contained in this box.

A. No more this box can contain is grammatically incorrect.
B. No more could be contained in this box is grammatically correct, but it is in the past tense, which does not make sense in the context of the question.
D. Nothing can be contained in this box is grammatically correct, but it is too strong. The box may be able to contain something, but it is full at the moment.

The sentence “The box can contain no more” means that the box is full and cannot hold anything else. This can be expressed in a number of ways, but the most concise and accurate way is “No more can be contained in this box.”