let's simply get the area of the larger square, and then get the area of the smaller square and subtract the area of the smaller square from that of the larger square, what's leftover is the shaded region.
[tex]\stackrel{\textit{area of the larger square}}{(4x-6)(4x-6)\implies \stackrel{F~O~I~L}{16x^2-48x+36}} ~\hfill \stackrel{\textit{area of the smaller square}}{(x)(x)\implies x^2} \\\\[-0.35em] ~\dotfill\\\\ (16x^2-48x+36)~~ - ~~(x^2)\implies 15x^2-48x+36 \\\\\\ 3(5x^2-16x+12) \implies 3(5x-6)(x-2)[/tex]
