Use a substitution. (Turn the problem into a factorable quadratic)

let a = y^2

Then, 81a^2-72a+16 is the new equation using a (since a^2 = y^4)

Now to factor, you need two numbers whose product is (81x16=1296) and whose sum is -72 (-36 and -36)

Factor by grouping:

81a^2 - 36a - 36a + 16

9a(9a - 4) - 4(9a - 4)

(9a - 4)(9a - 4)

Resubstiture a = y^2

(9y^2-4)(9y^2-4)