Finding the Determinants for Matrix

The question: https://gyazo.com/005997e8069185fb56235fe15ef10e0e

I did manage to successfully find the answers for AB, |A| and |B| and |AB| but I'm having some difficulty in properly re-arranging the answer for |AB| to equal |A||B|.
For |A||B| I got (ad-bc)(eh-fg) and for |AB| it was (ae+bg)(cf+ch) - (af+bh)(ce+dg)

Not exactly sure how I'm supposed to completely simplify it to get |A||B|

The only thing you can realistically do is to expand and simplify both versions and show that they are the same. However, you have a small error in you expression for |AB|. Check the term (cf+ch) - it should be slightly different.