12x^2y^3 = 2 * 2 * 3 * x * x * y * y * y
8xy^2 = 2 * 2 * 2 * x * y * y
The GCF is made up of the factors that appear in both 12x^2y^3 and 8xy^2. Both of those have two 2's, an x, and 2 y's, so the GCF is 2 * 2 * x * y * y = 4xy^2
Answer: The GCF of 12x^2y^3 and 8xy^2 is 4xy^2.