If his Fox News is on Cable channel 64, then you can't do anything about it. CATV Hyperband channel 64, no matter whether it's NTSC analog or ATSC QAM Digital, covers a 6MHz wide bandwidth between 462 and 468MHz. If you transmit anywhere in there, (GMRS) it will overload the TV or converter box.
Likewise, if you are transmitting in the 70cm ham band, depending on what frequency you are using, you will wipe out Cable channel 59, 60, or 61. the 2-Meter ham band rides on the same band as Cable channel 18, and MURS will wipe out channel 19.
NOTE: Cable channels above 14 are NOT the same frequencies as over-the-air TV channels above 14. Also note that with digital TV, the station can display whatever "virtual channel" they want you to see. Perhaps your local CBS affiliate still advertises themselves as "News-4", even though they switched to RF channel 27 over 19 years ago. Cable systems like to call digital channels much higher numbers such as "Hyper-tier 653" because it makes them sound bigger than they actually are - makes you think they have more channels out there that you just don't pay enough to get.
Here is a list of actual frequencies vs. channel numbers for Standard, IRC, and HRC type cable systems, along with standard over-the-air broadcast.
The visual carrier frequency is shown in this chart. TV is transmitted in Vestigial Sideband mode, meaning a full carrier and upper sideband, but the lower sideband is rolled off 1MHz below the carrier. The lower edge of the channel is 1.25 MHz below the visual carrier and the upper edge is 4.75 MHz above the visual carrier.