How to prove identities of a boolean equation?
Your approach looks unnecessarily complicated. 

The first point of simplification will be on the most complex term which is \$(\overline{\bar{b} + ac})\$ . Apply de-morgan's law there and reach the shortest expression (You may have to apply it twice).

Then all you have to do is to simply follow the distributive law on the three terms left with, and single out the common terms. You should be reaching the answer in a minute.