The problem is to factor the expression $xy + 3y + 2x + 6$.

1. Problem Description

The problem is to factor the expression $xy + 3y + 2x + 6$.

2. Solution Steps

We can factor by grouping. We group the first two terms and the last two terms:

$(xy + 3y) + (2x + 6)$.

Now, we factor out the greatest common factor (GCF) from each group. From the first group, the GCF is $y$, and from the second group, the GCF is $2$.

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

Now we have two terms, each containing a factor of $(x + 3)$. We can factor out $(x + 3)$ from both terms:

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

3. Final Answer

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