\(81\left(y-4\right)^2-9x^2-36x-36=9\left\{9\left(y-4\right)^2-\left(x+4\right)^2\right\}=9\left\{3\left(y-4\right)-\left(x+4\right)\right\}\left[3\left(y-4\right)+\left(x+4\right)\right]\)
\(=9\left(3y+12-x-4\right)\left(3y+12+x+4\right)=9\left(3y-x+8\right)\left(3y+x+16\right)\)