Why rear sprocket of motorcycle is bigger than front?

It's a simple math between the engines speed (rpm) v.s. the rear wheels speed (rpm).

The bicycle runs 20km/h where the motorbike runs more than 200km/h

On a bicycle where the engine (You) not exceeds much more than 50rpm do the sprocketsizes need to be opposite arranged to get the bicycle to drive with 20km/h (= 333 meter/minut => about 150rpm of the rearwheel).

In contradiction runs the rearwheeel of the motorbike easily more than 1.600rpm, but this by the help of an engine that often are able to rotate more than 12.000rpm.

To the math comes the fact that the motorcycle engine really isn't that powerfull when it comes to the figure of torque (@ rotating power):

Torque is easiest explained as the weight wich a bicyclist jogs in the pedal with, multiplied with the length of the pedal-arm:

A 80kg heavy bicyclist jogging on a 25cm (=1/4 meter) long pedal produces a torque of 20kg/m wich only the biggest motorbike-engines can match, but helped by the high revolutions on the engine it is able to reduce the rpm's towards the rearwheel, and very practic: the torque rises together with the decent rpm's amking higher speed possible!

The compleate story includes some gears inside the engine, but the explanation to the question is the same whether those details is brought to the table or not.