Answer: \(x=1\) or \(x=-1.5\).

Split the equation into the two possible cases.

If \(3x+2\geq0\), then

\(3x+2=x+4.\)

So

\(2x=2,\qquad x=1.\)

This satisfies \(3x+2\geq0\).

If \(3x+2\lt0\), then

\(-(3x+2)=x+4.\)

So

\(-3x-2=x+4,\qquad -4x=6,\qquad x=-\frac32.\)

This satisfies \(3x+2\lt0\).

Hence

\(\boxed{x=1\quad\text{or}\quad x=-1.5}.\)