To simplify the expression 3x^3y^4 - 6xy^5 ÷ 3xy^2, we can divide each term separately.

First, let's divide 6xy^5 ÷ 3xy^2:
6xy^5 ÷ 3xy^2 = (6/3) * (x/x) * (y^5/y^2) = 2 * 1 * y^(5-2) = 2y^3

Now, we can substitute this result back into the original expression:
3x^3y^4 - 2y^3

So, the simplified expression is 3x^3y^4 - 2y^3.