E is the midpoint of CD.
∴ Vector EC=( 1/2) Vector DC=( 1/2) Vector AB.
F is the bisector of BC
∴ vector CF=(2/3) vector CB=(2/3) vector DA=(-2/3) vector AD.
∴ vector EF=( 1/2) vector AB+(-2/3) vector AD
Option d
You can ask questions if you don't understand. If it helps, please adopt it. Thank you!