Factorize the expression 2bx + 6by.

The expression is $2bx + 6by$.
The terms are $2bx$ and $6by$.

First, find the GCF of the numerical coefficients: 2 and 6.
The GCF of 2 and 6 is 2.

Next, find the GCF of the variables.
Both terms contain the variable $b$.
The variable $x$ is only in the first term.
The variable $y$ is only in the second term.
So, the common variable factor is $b$.

The overall GCF for the expression is $2b$.

Divide each term by the GCF, $2b$:

$$\frac{2bx}{2b} = x$$ $$\frac{6by}{2b} = 3y$$

Combine the GCF with the results from Step 2.

$$2b(x + 3y)$$