With any question in this form, we always first completely isolate the 'log' part of the function, and then solve from there. To get the log8(2x+7) alone, we solve for it just as we would solve for any other variable.
3log8(2x+7) = 2
Here we need to remove the log term. We know that logb(x) = n is the same thing as saying bn = x. So, we raise 8 to the power of both sides. This gets rid of the log8 term. So:
2x + 7 = 82/3
2x+7 = 4 and from here we can solve like any other equation
2x = -3
x = -3/2