So your function is 2/3 * |x+1| -3 if I understood correctly. So if you need to graph it, go step by step: First of all, replacing "x" with "x+1" shifts the Graph 1 unit to the left. So e.g. |x+1| would look like |x|, but each point is shifted unit to the left. Now lets multiply by 2/3. That just means we multiply every y-value by 2/3. Which in turn just means our slope gets slightly shallower.
Finally, subtracting 3 shifts the graph 3 units down.