Formula use:

a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)

Explanation

Here, given expression is :
\left(x+y\right)\ \left(x-y\right)\left(x^2+xy+y^2\right)\ \left(x^2-xy+y^2\right)
\rightarrow\left(x-y\right)\ \left(x^2-xy+y^2\right)\ \left(x+y\right)\ \left(x^2+xy+y^2\right)
\rightarrow\left(x^3-y^3\right)\left(x^3+y^3\right)
\rightarrow\{x^3\left(x^3+y^3\right)-y^3\left(x^3+y^3\right)\}
\rightarrow\left(x^6+x^3y^3-x^3y^3-y^6\right)
\therefore x^6-y^6
Ans: x^6-y^6.