Step 1 :Given the algebraic expression \(-x^{2}-4 x y+4 y^{3}\) and the values of the variables x=-2 and y=-1.
Step 2 :Substitute the given values of x and y into the expression. This gives us \(-(-2)^{2}-4(-2)(-1)+4(-1)^{3}\).
Step 3 :According to the order of operations, first calculate the exponents. This gives us \(-4-4(-2)+4(-1)\).
Step 4 :Next, perform the multiplication and addition operations. This gives us \(-4+8-4\).
Step 5 :Finally, perform the addition and subtraction operations. This gives us -16.
Step 6 :So, the simplified value of the expression \(-x^{2}-4 x y+4 y^{3}\) for x=-2 and y=-1 is \(\boxed{-16}\).