Given Iines are
$$
\begin{aligned}
& \mathbf{r}=-4 \hat{\mathbf{i}}-\hat{\mathbf{k}}+t(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \\
& \text { and } \quad \mathbf{r}=6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}+s(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}) \\
& \therefore \quad \mathbf{a}_1=-4 \hat{\mathbf{i}}-\hat{\mathbf{k}}, \mathbf{b}_1=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}} \\
& \mathbf{a}_2=6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}_2=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}} \\
&
\end{aligned}
$$
Now, $\mathbf{a}_2-\mathbf{a}_1=10 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathbf{k}}$
$$
\mathbf{b}_1 \times \mathbf{b}_2=\left|\begin{array}{ccc}
\hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\
3 & -2 & -2 \\
1 & -2 & 2
\end{array}\right|=-8 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}
$$
$$
\begin{aligned}
\therefore \quad\left|\mathbf{b}_1 \times \mathbf{b}_2\right| & =\sqrt{(-8)^2+(-8)^2+(-4)^2} \\
& =\sqrt{64+64+16}=12 \\
\text { and }\left(\mathbf{a}_2-\mathbf{a}_1\right) & \cdot\left(\mathbf{b}_2 \times \mathbf{b}_2\right) \\
& =(10 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \cdot(-8 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}) \\
& =-80-16-12=-108
\end{aligned}
$$
and $\left(a_2-a_1\right) \cdot\left(b_2 \times b_2\right)$
$$
\begin{aligned}
& =(10 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \cdot(-8 \hat{\dot{\mathrm{i}}}-8 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}) \\
& =-80-16-12=-108
\end{aligned}
$$
$\therefore$ Required distance
$$
=\left|\frac{\left(\mathbf{a}_2-\mathbf{a}_1\right) \cdot\left(\mathbf{b}_1 \times \mathbf{b}_2\right)}{\left|\mathbf{b}_1 \times \mathbf{b}_2\right|}\right|=\left|\frac{-108}{12}\right|=9
$$