A man travels:

$12$ kilometres northeast

then:

$20$ kilometres $30 \degrees$ west of north

then:

$18$ kilometres $60 \degrees$ south of west.

Assuming the curvature of the Earth to be negligible at this scale, at the end of this travel, he is $14.7$ kilometres in a direction $45 \degrees 49'$ west of north from his starting point.

Proof

By plotting the points in a graphics package, or on paper with a ruler and protractor:

$\blacksquare$