Ayre, Patricia y yo pintamos un retrato de nuestra profesora.
"Patricia y yo" is Patricia and I, or we. The conjugation for we is the verb ending in -amos.
The name already suggests that the "personal" a is needed for people - So we will choose an option that has a person with its object. (so not with "reglas" )
It's not needed for possession, so it will not appear with the sentences that have "tener" in them.
It is needed in the last option: mira a Pablo.
Also, we will need it for "dile al encargado" because the encargado is a person in charge. But then it will bind with "el" forming "al" - so not "a" anymore