We are given:
The tuning fork vibrates at 15660 oscillations per minute
Period of one back-and forth movement:
the given data can be rewritten as:
1 minute / 15660 oscillations
60 seconds / 15660 oscillations (1 minute = 60 seconds)
dividing the values
0.0038 seconds / Oscillation
Therefore, one back and forth vibration takes 0.0038 seconds