the way that you factor 18c^2 -128 is you :
list the prime factors of 18c^2 and 128
18c^2:2*3*3*c*c
128: 2*2*2*2*2*2*2
then you circle the to prime factors that are alike on top and bottom which is 2
so your final answer is :
2(9c-64)
the way to check your work is you distrbute then you will get the equation that you started with.