Infinite solutions only happens when both sides are equal. So in order for this equation to have infinite solutions, both sides must be equal at the end.
2(x+8)=2x+8
Hopefully, you can already see it is not infinite solutions here because the first step is to distribute and 2 times 8 is not 8.
2x+16=2x+8
So no, this is not infinite solution.
16=8