Question

we are trying to figure out how they arrived at the 8x

Answer 1

$x=2,y=10$

1) Since when we examine the question, we can come up with a system of the following equations:

$\begin{gathered} y=12-x \\ 24x+16y=208 \end{gathered}$

2) So, we can solve this system by the Substitution Method plugging into the 2nd equation the first one, i.e. y=12-x:

$\begin{gathered} 24x+16y=208 \\ 24x+16(12-x)=208 \\ 24x+192-16x=208 \\ 24x-16x+192=208\:\:\:Combine\:like\:terms \\ 8x+192=208 \\ 8x+192-192=208-192\:\:Subtract\:192\:from\:both\:sides \\ 8x=16\:\:Divide\:both\:sides\:by\:8 \\ \frac{8x}{8}=\frac{16}{8} \\ x=2\:Redwood\:Trees \\ y=12-x\Rightarrow y=12-2\Rightarrow y=10\:spruce\:trees \\ \end{gathered}$

Note that when we combine like terms we come up with a single term with the same variable