Cannot figure out the convolution operation in this problem A linear system S has the relationship $y[n]=\sum_k {x[k]*g[n-2k]}$, k ranging from $-\infty$ to $\infty$, between its input $x[n]$ and output $y[n]$, $g[n]=u[n]-u[n-4]$. 

Determine $y[n]$ when $x[n]=\delta[n-1]$. 

I know that the convolution operation can only be applied when both the operands have the same value of $n$ and that : 

$$
y[n]=x[n]*h[n]=\sum_k {x[k]h[n-k]}
$$

I don't understand how $x[k]$ and $g[n-2k]$ can be convolved with each other, when they do not have the same inputs. How do I perform discrete convolution on $x[k]$ and $g[n-2k]$?
Hint:

For which values of $k$ is $x[k]=\delta[k-1]$ not equal to zero? How does that simplify the given sum?