Answer
The intercept with $y$ axis is $y=6$. There are two intercepts with $x$ axi: $x=6$ and $x=-6$. The graph is symmetric and shown on the figure.
Work Step by Step
To find the intercept with $y$ axis put $x=0$ and solve for $y$:
$$y=6-|0| = 6-0 = 6.$$
To find the intercept with $x$ axis put $y = 0$ and solve for $x$:
$$0=6-|x|.$$ Put $|x|$ to the left side to get
$$|x| = 6.$$
This is possible for two values of $x$:
$$x=-6\text{ and } x=6$$
because the absolute value notation "removes" the minus sign from the number if it's there.
To test the symmetry we put $-x$ instead of $x$:
$$y(-x) = 6-|-x| = 6-|x| = y(x)$$
where we used the fact that $|x| = |-x|$ for every number $x$ because the absolute value would just "eat" the minus sign if it appears in front of a number inside the $||$ brackets. Since $y(x)=y(-x)$ the graph is symmetric.
