Answer
$(3,6)\cdot(-8,4)=3(-8)+6(4)=-24+24=0$
Work Step by Step
If the vectors are perpendicular, their dot product must be zero.
Dot product$=(3,6)\cdot(-8,4)=3(-8)+6(4)=-24+24=0$.
Therefore, $3\textbf {i}+6\textbf {j}$ and $-8\textbf {i}+4\textbf {j}$ are perpendicular.