-80=8b-15+5b

How do I solve this and what does check mean?

-80=8b-15+5b

-80 + 15 = 13b
or
13b = -65
b = -5

Solving an equation means finding that value of the variable which makes the original equation a true statement.
We found that value to be b = 5

Now sub that value into the left side and the right side of the ORIGINAL equation.

LS = -80
RS = 8(-5) - 15 + 5(-5)
= -40 - 15 - 25
= -80
since we have shown LS = RS for b = -5
we have verified that our answer is correct