To simplify, we will have to factor the numerator of the first fraction and the denominator of the second fraction.
#\frac { x ^ { 2} + x - 12} { color(blue)(x) color(green)(y ^ { 2}) } \cdot \frac { color(blue)(x ^ { 7})color(green)( y )} { x ^ { 2} + 7x + 12}#
#=\frac { cancel((x+4))(x-3)} { color(blue)(x) color(green)(y ^ { 2}) } \cdot \frac { color(blue)(x ^ { 7})color(green)( y) } { cancel((x+4))(x+3)}#
We see that the #(x+4)# from the top and the bottom cancel, but also an #xy# factor (from the denominator of the first fraction and the numerator of the second fraction).
Thus, this simplifies to:
#=\frac { (x-3)} { y} \cdot \frac { x ^ { 6}} { (x+3)}#
#=\frac { x ^ { 6}(x-3)} { y(x+3)}#
