can you help me please?
$\displaystyle -4x^{2} - 4xy - 3y^{3} = -192$
Taking the derivative of both sides:
$\displaystyle -8x - 4(y + xy') - 9y^{2}y' = 0$
The middle term -4(y + xy') is just using the product rule in differentiating.
Solve for y' at (-4,4) and that will be your slope value.
You should be able to go from there?