This problem written in that way, isn't interesting, it can be done 'manually'. From the other hand, this is a special case of a strong thing : Olson's theorem. Thinking generally, we can prove much more than this task requires.

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grade it is the class?

a general version -- it is well known that ,given (2n-1) positive integers. show that , it is possible to get n from them , such that, their sum is divisible by n. put n=6 and done!

I'm still not sure how to do it. :/

See here https://www.renyi.hu/~p_erdos/1961-25.pdf