The distance between the 1st and 20^th street light is 38 m.

Since there are 20 street lights, there are 20- 1 = 19 gaps between them.

Then, 19 × gap between two street lights = 38

Thus, each street light has a gap of 2 m between them.

The 3rd and 12th street light has 9 gaps between them.

Then, Required distance = 9 × 2 m = 18 m

Hence, option b.