Graphical DT Convolution
To elaborate the point of my comment:

What you did there is a kind of circular convolution, where you thought of the impulse response $h(t)$ as periodic, i.e. the system triggered by $\delta(0)$ would oscillate until infinity. The periodicity is represented by your "wrapping around" the impulse response. The output you calculated is actually just one period of the output signal.

This is different from the linear convolution that the task formulation obviously expects to be applied here. With the linear convolution, the impulse response is thought to be the graph representing $h(n)$ padded by zeros from $-\infty$ to $0$ and from $3$ to $\infty$. Here, if the system is triggered by $\delta(0)$, you would get $h(n)$ and then all zeros to infinity.