Step 1 :Subtract the corresponding terms in the two polynomials.
Step 2 :Subtract $8 y^{2}$ from $2 y^{2}$ to get $-6 y^{2}$.
Step 3 :Subtract $-5 y$ from $7 y$ to get $12 y$.
Step 4 :Subtract $7$ from $11$ to get $4$.
Step 5 :Combine the results to get the final polynomial $-6 y^{2}+12 y+4$.
Step 6 :\(\boxed{-6 y^{2}+12 y+4}\) is the final answer.