First of all, distribute the -2:
-2(5+6c)= -10+(-12c)=-10-12c
So now you have:
-10-12c+16=-90
Simplify by adding -10 and 16 = 6
6-12c=-90
Subtract 6 from both sides:
-12c=-96
Divide both sides by -12:
c=8 (Answer)
To check your work, plug it back in.
-2(5+6(8))+16=-90
-2(5+48)+16=-90
-2(53)+16=-90
-106+16=-90
-90=-90
since both sides are equal, you know this is the correct answer.