Please see the work below.
Work Step by Step
We know that an acid base reaction is the one in which a proton transfer takes place. $NH_4Cl$ exists as $NH_4^+$ and $Cl^-$, and from $NH_3$ and $HCl$, a proton is transferred from $NH_4^+$ to $Cl^-$. Hence, the given reaction is an acid-base reaction.