$$ h[n]= \left( \frac{8}{9} \right) ^n u[n-3] $$
And the function is:
$$x[n] =
\begin{cases}
2 & \text{if } 0 \leq n \leq9, \\
0 & \text{ else}.
\end{cases}$$
In order to find the convolution sum $y[n]=x[n]*h[n]$:
$$y[n]=\sum_{n=-\infty}^{+\infty}{x[n]\cdot h[k-n]}$$
$$y[n]=\sum_{n=-\infty}^{+\infty} {x[n]\cdot \left(\frac{8}{9}\right)^n\cdot u[k-3-n]}$$
How do I proceed from here?
In essence, how do I evaluate a finite sum for these conditions?