The problem asks to expand the product of two binomials: $(2x + y)(4x + 3y)$.

1. Problem Description

The problem asks to expand the product of two binomials: $(2x + y)(4x + 3y)$.

2. Solution Steps

We can use the distributive property (also known as FOIL method) to expand the expression.

$(2x + y)(4x + 3y) = (2x)(4x) + (2x)(3y) + (y)(4x) + (y)(3y)$

Now, we multiply the terms:

$(2x)(4x) = 8x^2$

$(2x)(3y) = 6xy$

$(y)(4x) = 4xy$

$(y)(3y) = 3y^2$

Substitute these back into the equation:

$8x^2 + 6xy + 4xy + 3y^2$

Combine the like terms (the $xy$ terms):

$6xy + 4xy = 10xy$

So the expression becomes:

$8x^2 + 10xy + 3y^2$

3. Final Answer

$8x^2 + 10xy + 3y^2$