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Can anyone help me this problem? I know the sum of consecutive integers is n(n+1)/2, but I don't know how to move forward from here.

If 738 consecutive integers are added together, where the 178th number in sequence is 4,256,815, what is the remainder when this sum is divided by 6?

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    You already had a perfectly good answer from the previous time you asked the same question. Now I have wasted my time. Sad! – 2017-02-27

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The sum of any $6$ consecutive integers is $$ 6n+1+2+3+4+5 = 6n+15 \equiv 3 \pmod 6 $$ Since $738=123\cdot 6$ you have $123$ such groups ...