Dubya

$y = |x| + 2|x+1| - 3|x+2| + 4|x+3|$

It's given that $y = \mathscr{E}$ has only two intersections with the above equation. What is the minimum integral value of $\mathscr{E}$ that meets this condition?

$$ Notation : $| \cdot |$ denotes the absolute value function .