ABS(2x + y) - ABS(x + 3y) = 8
ABS = absolute value
I need to know where to start
When dealing with absolute value, you have to be aware of the folling fact-that $\displaystyle \mid{x}\mid=\mid{-x}\mid=x$ So, therefore $\displaystyle x$ can have 2 different values, but the corresponding value of $\displaystyle y$, or $\displaystyle f(x)$ will have only one. So knowing that....
We've got to set up different possibilities for the given expressions.
$\displaystyle \mid2x+y\mid=\pm(2x+y)$ and $\displaystyle \mid{x+3y}\mid=\pm(x+3y)$.
So, with this, can you take it from here?