What is the distance in cm between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm?

There are 2 possibilities :

Both chords on opposite side of the centre.

Both side on the same side from the centre.
Opposite side:

Perpendicular from the centre to the chord, bisects the chord.

Hence PB = 12 and QA = 16.

Now, apply Pythagoras theorem.

OP2 = OB2 - PB2 = 400 – 144 = 256. OP = 16.

OQ2 = OA2 - QA2 = 400 – 256 = 144. OQ = 12.
Hence, the distance is sum of OP and OQ is 28.

Same side :

Then, you will get OP as 16 and OQ as 12 (explained above).
Since they are on the same side, 
Hence, the distance between them is 
(16 – 12) = 4.