The given complex expression is
[tex](-2-4i)(5+6i)[/tex]
The expression can be expanded as follows
[tex](-2-4i)(5+6i)=-2(5+6i)-4i(5+6i)[/tex]
Multiply the numbers
[tex]\begin{gathered} -2(5+6i)-4i(5+6i) \\ =-10-12i-20i-24i^2 \end{gathered}[/tex]
Simplify further
[tex]\begin{gathered} -10-12i-20i-24i^2 \\ =-10-32i-24i^2 \end{gathered}[/tex]
But
[tex]i^2=-1[/tex]
Hence, it follows
[tex]\begin{gathered} -10-32i-24i^2 \\ =-10-32i-24(-1)^{} \\ =-10-32i+24 \\ =14-32i \end{gathered}[/tex]
Therefore, the answer is
[tex]14-32i[/tex]
