Let us consider a signal with an initial intensity of I, that travels through a medium and the final intensity is F. I have considered an electromagnetic signal moving through an appropriate medium.
The attenuation is expressed in terms of decibels and given by the formula:
Attenuation = 10* log (I / F)
In the question the signal travelling through the transmission medium loses 3/4 of its power.
If the initial power was I, the final power is I/4.
Substituting this in the formula for attenuation we get:
Attenuation = 10 * log (I / (I/4))
=> 10* log (4I/I)
=> 10* log 4
Therefore the attenuation is 6.02 dB.