The quadrature detector on your imager has a reference signal of 63.85 MHz coming into one of the channels. The signal channel has a signal of 63.86 MHz coming into it. What frequency or frequencies will be coming out of the detector?

The DBM within the quadrature detector produces frequencies at (ν - νo) and (ν + νo).
The filter within the quadrature detector removes (ν + νo).

ν = 63.86 MHz, and νo = 63.85 MHz.

Therefore, (ν - νo) = 10 kHz.