My approach was different.
If in 12 min a bus overtakes the cyclist, while in 4 min they both cross each other. So, at the end of 12th min, the overtaking bus will meet the 3rd bus coming from the opposite side, which means there are 2 buses gone in the 12 min time period.
We are given speeds of buses and cyclist constant. So, in 12 min, if two buses passes at an interval of 6 min.
What would be the answer with your approach if it were 2 minutes instead of 4?
the answer is 4 here, it has asked time interval between two buses, first bus will meet at 8th min, and 2nd bus will meet at 12th min, so difference is 4 minutes...
Relative velocity concept, cyclist speed is assumed to be 0.
Buses speed are constant, so first bus will met at 8th min, second at 4th minutes. difference is 4 Min.