First, let's simplify the expression (3+4y)(4-3y):

(3+4y)(4-3y)
= 3(4) + 3(-3y) + 4y(4) + 4y(-3y)
= 12 - 9y + 16y - 12y^2
= -12y^2 + 7y + 12

Now, let's square the result:

(-12y^2 + 7y + 12)^2
= (-12y^2 + 7y + 12) * (-12y^2 + 7y + 12)
= 144y^4 - 168y^3 + 72y^2 + 84y^3 - 98y^2 - 42y + 144y^2 - 168y + 72
= 144y^4 - 84y^3 + 188y^2 - 210y + 72

Therefore, the expression (3+4y)(4-3y)-16y squared is equal to 144y^4 - 84y^3 + 188y^2 - 210y + 72.