2 determinants are given in which one determinant is expressed as the product of other two determinants . Can you explain the method by which that process is accomplished in detail ?

There is a concept called product of determinants, similarily like product of matrices, in determinants we have flexibilty like we can multiply row-row, row-column, column-column, column-row instead in matrix we are only allowed row-column multiplication.
So in this way by hit and trial method you have to think of two determinants which if we multiply will get the same determinant in the given question.