from the question;
we are given
[tex]\begin{gathered} P(x)=4x^2\text{ + 6x - 9} \\ Q(x)=-7x^2\text{ - 12x + 8} \end{gathered}[/tex]we are to find the sum of P(x) and Q(x), that is
[tex]\begin{gathered} P(x)\text{ + Q(x)} \\ =4x^2+6x-9+(-7x^2\text{ -12x +8)} \\ =4x^2\text{ + 6x - 9 -7x}^2\text{ -12x + 8} \\ =\text{ }4x^2-7x^2\text{ + 6x - 12x - 9 + 8 } \\ =-3x^2\text{ -6x - 1} \end{gathered}[/tex]Therefore, the sum of P(x) + Q(x) is
[tex]-3x^2\text{ -6x - 1}[/tex]