How to solve for the lhs to get the rhs?

see attached , first convert cycle into permutation then do composition then again convert permutations into cycles .. similarly you can do other part... if any doubt then as...

Any doubt then you can ask.

Transpositions are of order 2 then square of (ab) is identity. first two are easily done now. for last see the image of element in first cycle then in the second. for example imag...