This lesson builds the subjunctive on the ils/elles form of the present: remove -ent, then add the subjunctive endings.
The pattern
ils parlent → parl- → que je parle. The endings are -e, -es, -e, -ions, -iez, -ent, so the nous and vous forms match the imparfait: que nous parlions, que vous parliez. An -ir verb of the finir type carries its -iss- across: qu'ils finissent → que je finisse.