Two similar solids have a scale factor or 6: 7
what is ratio of their volumes, expressed in lowest terms?

You cube each of the numbers
that is 6^3  : 7^3 
= 216:343

For similar solids, the ratio of the volumes given the ratio of the corresponding sides (in this problem given as scale factor), can be solved by raising that ratio to exponent 3. That is, 
                   ratio of volumes = (6/7)³
which will give us an answer of
                    ratio of volumes = 216/343