The output of the mixer will contain the frequencies:
Fx, Fy, Fx+Fy, Fx-Fy, and probably many others such as 2Fx-Fy, 2Fy-Fx etc.
The task of the filter is to remove everything except Fx-Fy which will be the lowest frequency in the output of the mixer, hence the use of a low-pass filter.
What you need to consider is, what frequencies were you using in your practicals?
What is the cutoff frequency of the low-pass filter?