A network administrator enters the following command into Router3: ip route 172.16.0.0 255.255.255.0 S1/1/0. Router3 then receives a packet that is destined for 172.16.0.22/24. what does Router3 do next to process the packet?

R3 will have S 172.16.0.0/24 in its routing table.

When a packet with dip 172.16.0.22 is received on any interface of R3, it will be matched with the above entry in routing table and router will forward it to next-hop / exit interface. As you have a point-to-point interface as outgoing, R3 will forward the packet on exit interface s1/1/0. If next-hop is given for serial interface an unnecessary routing table lookup will be necessary.

R3 will check 172.16.0.22/24 in its routing table. If it found the entry it will forward it to next-hop otherwise it will drop.