Filter to eliminate a 60 Hz frequency range
The OP is trying to implement a notch filter with a 3 tap FIR filter (as restricted by the problem he is trying to solve). It must be noted that this would result in a very poor filter implementation: It will reject 60 Hz perfectly but will have unavoidable attenuation over a very broad section of the desired passband range. An actual practical implementation would be done with an IIR approach in order to provide a tight notch, as demonstrated by this link: Transfer function of second order notch filter
As a hint to determine the filter within this FIR restriction, as an exercise only and of no real practical value proceed as follows:
Take the Z transform of the difference equation.
Determine the transfer function form as a polynomial ratio $H(z) = Y(z)/X(z)$
From this know that the frequency response is determined by restricting $z$ to the unit circle ($z= e^{j\omega}$) with $\omega$ extending uniquely over the normalized radian frequency from $-\pi$ to $+\pi$ which corresponds to $-f_s/2$ to $+f_s/2$ where $f_s$ is the sampling rate.
Given this is an FIR structure, the transfer function will result in simply a 2nd order polynomial in the numerator (whos roots are the &quot;zeros&quot; of the filter). Place the zeros of this polynomial such that they corresponds to the 60 Hz locations on the unit circle (+/- 60 Hz for a real filter, mapped to the angular frequency as described above), which would provide complete attenuation at f = 60 Hz.