Factorize the expression 4x2y - 16xy2 + 12xy

The expression is $4x^2y - 16xy^2 + 12xy$.
The terms are $4x^2y$, $-16xy^2$, and $12xy$.

First, find the GCF of the numerical coefficients: 4, $-16$, and 12.
The GCF of 4, 16, and 12 is 4.

Next, find the GCF of the variables.
For $x$: The lowest power of $x$ in the terms is $x^1$ (from $-16xy^2$ and $12xy$). So, $x$ is a common factor.
For $y$: The lowest power of $y$ in the terms is $y^1$ (from $4x^2y$ and $12xy$). So, $y$ is a common factor.

The overall GCF for the expression is $4xy$.

Divide each term by the GCF, $4xy$:

$$\frac{4x^2y}{4xy} = x$$ $$\frac{-16xy^2}{4xy} = -4y$$ $$\frac{12xy}{4xy} = 3$$

Combine the GCF with the results from Step 2.

$$4xy(x - 4y + 3)$$