Frequency and Beats -- help needed

A sonometer string and a tuning fork of frequency 256 Hz, when vibrating together, produce 4 beats per second. When the fork is slightly loaded, 6 beats are heard per second. The frequency of the string is
a) 248 Hz b) 252 Hz c) 260 Hz d) 250 Hz
Revered members, please help with the answer

The beat frequency equals the difference between the 2 main frequencies. Th difference is 4Hz.

Since the tuning fork has a frequency of 256Hz, the string could have a frequency of:
256+4=260Hz or
256-4=252Hz
So it must be is either answer b) or c).

Slightly loading the fork (adding something to increase its mass) will lower its frequency. (Just like using a thicker string on a musical instrument produces a lower frequency.) Loading the fork has increased the difference between the 2 main frequencies from 4Hz to 6Hz. This is only possible if the string's frequency is higher than the the tuning fork's. So the string's frequency is 260Hz - answer c).

The beat frequency is the absolute difference between the two frequencies, i.e.

4 = |256 - f_string|

so it could be that:
4 = 256 - f_string
or
4 = f_string - 256

so:
f_string = 252 or 260

When the fork is lightly loaded its frequency must go down, but how much is "lightly loaded"?

The solution is not unique for a beat frequency of 6: if the new loaded frequency of the fork is 254 Hz, f_string = 260 Hz. But if the loaded frequency of the fork is 246 Hz, f_string = 252 Hz.

To be sure you would have to do tests at different loads. A single test, without knowing the actual size of the load, is inconclusive.

Ask your teacher to pay more attention to his/her work.

well, 4 beats could be produced by a string of 252 or 256 Hz
but
loading the fork slows it down and since this give more beats the string must be the higher frequency one
so
260 Hz