Step 1: Recall what makes a Lewis acid or base.
A Lewis acid accepts an electron pair (it is electron-short). A Lewis base donates an electron pair (it has a lone pair). Something that is neither is electron-satisfied with no spare lone pair.
Step 2: Look at the hydride of X (Lewis acid).
$AlH_3$ has only six electrons around aluminium, so it is electron deficient and grabs electron pairs. That makes X = Al.
Step 3: Look at the hydride of Y (Lewis base).
$PH_3$ has a lone pair on phosphorus that it can donate, so it behaves as a Lewis base. That makes Y = P.
Step 4: Look at the hydride of Z (neither).
$SiH_4$ has a complete octet on silicon and no lone pair, so it neither accepts nor donates. That makes Z = Si.
Step 5: Check the other options.
$CH_4$ (carbon) is also neither, but the acid-base pair Al and P only line up with the set Al, P, Si.
Step 6: Conclusion.
So X, Y, Z are Al, P, Si. \[ \boxed{\text{Al, P, Si}} \]