explain why it is easier to hang a shopping bag from the crook of your elbow than to carry it suspended from your hand with your arm at 90 degree angle.

A weight at the elbow exerts a downward force on the elbow.

A weight at the hand, a perpendicular distance from the elbow, exerts a downward force and a bending moment.

So hanging a bag from the crook of your elbow puts less stress on your arm.