A man left home for a morning walk, went 12 km southwards, turned right and walked 8 km, again turned right and walked 12 km, then turned left and walked 10 km. How many kilometres must the man walk straight to reach home?

The man ends up 18 km due west of home, so a straight 18 km walk returns him.

Take home as (0,0); 12 km south reaches (0,-12).

Right turn faces west, 8 km gives (-8,-12).

Right again faces north, 12 km gives (-8,0).

Left faces west, 10 km gives (-18,0).

Straight-line distance to (0,0) = 18 km.