We use the FOIL technique: First Outside Inside Last $$\begin{aligned} \left({y^{3}-12}\right)^2&=\left({y^{3}-12}\right)\left({y^{3}-12}\right)\\ &={y^{6}-12y^{3}-12y^{3}+144}\\ &={y^{6}-24y^{3}+144} \end{aligned}$$ Alternatively, we might observe that this is the square of the difference of two terms, in which case we may use the formula $$(a-b)^2=a^2-2ab+b^2$$ and write $$\begin{aligned} \left({y^{3}-12}\right)\left({y^{3}-12}\right)&=\left(y^{3}\right)^2-2\cdot y^{3}\cdot 12+12^2\\ &={y^{6}-24y^{3}+144} \end{aligned}$$ which is the same result we obtained using the FOIL method.