Discrete time signals connected in series
You simply need to put $w[k]$ into $y[k]$:

$$w[k]=0.25x[k-2] \Rightarrow \begin{align}w[k-1]&amp;=0.25x[k-3]\\
 w[k-2]&amp;=0.25x[k-4]
\end{align}$$

\begin{align}
y[k] &amp;= 0.5w[k-1] + 0.5w[k-2]\\
&amp;=0.5\cdot0.25x[k-3] + 0.5\cdot0.25x[k-4]\\
&amp;= 0.125(x[k-3]+x[k-4])
\end{align}

You can directly read the impulse response from it.