We are given two equations: $4x + 2y = 16$ and $6x - 2y = 4$. We want to find the value of $y - x$.

1. Problem Description

We are given two equations: $4x + 2y = 16$ and $6x - 2y = 4$. We want to find the value of $y - x$.

2. Solution Steps

First, we can add the two equations to eliminate $y$:

$(4x + 2y) + (6x - 2y) = 16 + 4$

$10x = 20$

$x = \frac{20}{10} = 2$

Now that we have the value of $x$, we can substitute it into one of the equations to find the value of $y$. Let's use the first equation:

$4x + 2y = 16$

$4(2) + 2y = 16$

$8 + 2y = 16$

$2y = 16 - 8$

$2y = 8$

$y = \frac{8}{2} = 4$

Finally, we can calculate $y - x$:

$y - x = 4 - 2 = 2$

3. Final Answer

The value of $y - x$ is

2. The answer is B.