The problem is: given points $A(a, 6)$ and $B(2, a)$ lying on the line $4x + 2y = b$, determine the values of $a$ and $b$.

1. Problem Description

The problem is: given points $A(a, 6)$ and $B(2, a)$ lying on the line $4x + 2y = b$, determine the values of $a$ and $b$.

2. Solution Steps

Since points $A(a, 6)$ and $B(2, a)$ lie on the line $4x + 2y = b$, we can substitute the coordinates of each point into the equation.

For point $A(a, 6)$:

$4a + 2(6) = b$

$4a + 12 = b$

For point $B(2, a)$:

$4(2) + 2a = b$

$8 + 2a = b$

Now we have a system of two equations with two variables $a$ and $b$:

$4a + 12 = b$

$2a + 8 = b$

Since both expressions are equal to $b$, we can set them equal to each other:

$4a + 12 = 2a + 8$

$4a - 2a = 8 - 12$

$2a = -4$

$a = -2$

Now we can substitute the value of $a$ back into either equation to find $b$. Let's use the second equation:

$2a + 8 = b$

$2(-2) + 8 = b$

$-4 + 8 = b$

$b = 4$

3. Final Answer

$a = -2$ and $b = 4$.