1. **State the problem:** Find the greatest common factor (GCF) of the terms $4x^2y$ and $6xy$. 2. **Recall the formula and rules:** The GCF of two terms is the product of the lowest powers of all common factors (numbers and variables) in the terms. 3. **Factor each term:** - $4x^2y = 2^2 \times x^2 \times y$ - $6xy = 2 \times 3 \times x \times y$ 4. **Identify common factors:** - For numbers: common prime factors are $2$ - For variables: common factors are $x$ and $y$ 5. **Choose the lowest powers:** - For $2$: lowest power is $2^1 = 2$ - For $x$: lowest power is $x^1 = x$ - For $y$: lowest power is $y^1 = y$ 6. **Multiply the common factors:** $$\text{GCF} = 2 \times x \times y = 2xy$$ **Final answer:** The greatest common factor of $4x^2y$ and $6xy$ is $2xy$.