Answer
$$f\left( { - 1,2} \right) = - 19{\text{ and }}f\left( {6, - 3} \right) = - 255$$
Work Step by Step
$$\eqalign{
& f\left( {x,y} \right) = - 4{x^2} + 6xy - 3 \cr
& {\text{find }}f\left( { - 1,2} \right).{\text{ substitute }} - 1{\text{ for }}x{\text{ and }}2{\text{ for }}y \cr
& f\left( { - 1,2} \right) = - 4{\left( { - 1} \right)^2} + 6\left( { - 1} \right)\left( 2 \right) - 3 \cr
& {\text{simplifying}} \cr
& f\left( { - 1,2} \right) = - 4 - 12 - 3 \cr
& f\left( { - 1,2} \right) = - 19 \cr
& \cr
& {\text{find }}f\left( {6, - 3} \right).{\text{ substitute 6 for }}x{\text{ and }} - 3{\text{ for }}y \cr
& f\left( {6, - 3} \right) = - 4{\left( 6 \right)^2} + 6\left( 6 \right)\left( { - 3} \right) - 3 \cr
& {\text{simplifying}} \cr
& f\left( {6, - 3} \right) = - 144 - 108 - 3 \cr
& f\left( {6, - 3} \right) = - 255 \cr} $$
