To simplify the expression, we can use the distributive property to expand it:

(6x^2 + y)^2 (y^2 - 6x^2) = (6x^2 + y)(6x^2 + y)(y^2 - 6x^2)

Expanding this expression further, we can use the FOIL method:

(6x^2 + y)(6x^2 + y)(y^2 - 6x^2) = (36x^4 + 12x^2y + 12x^2y + y^2)(y^2 - 6x^2)

Simplifying the expression inside the parentheses:

(36x^4 + 24x^2y + y^2)(y^2 - 6x^2)

Now, we can use the distributive property again to expand this expression:

36x^4(y^2 - 6x^2) + 24x^2y(y^2 - 6x^2) + y^2(y^2 - 6x^2)

Simplifying each term:

36x^4y^2 - 216x^6 + 24x^2y^3 - 144x^4y + y^4 - 6x^2y^2

So, the simplified expression is:

36x^4y^2 - 216x^6 + 24x^2y^3 - 144x^4y + y^4 - 6x^2y^2