**Solution:**

Let the speed of cyclist be x

Let's say the distance between the buses is d and the speed of the bus is y

=>Interval = d/y

Relative speed b/w bicycle and bus = y-x as they are moving in same direction

Since, every 12 minutes a bus overtakes cyclist,

We have, t= d/ y-x = 12

=>d=12y-12x

Every 4 minutes cyclist meets an oncoming bus

=>Relative speed b/w bicycle and oncoming bus = y +x (opposite direction implies addition of speed)

=> d/x +y =4

=>d=4x + 4y

12y-12x = 4x + 4y

=>8y=16x

=>y=2x=>x=y/2

=>d=12y-12x=12y -6y =6y (since x=y/2)

=> Interval = d/y = 6y/y = 6

**(option b)**