Hi,
The TWR-K65F180M board user guide shows below info:

So, we need to use USB HS with on-board Micro USB connector J15 and USB FS with TWR-SER board J14.
I do a test with MCUXpresso SDK V2.2 for TWR-K65F180M board with [usb_keyboard2mouse] demo, which using FS USB as USB host and HS USB as USB device.
..\SDK_2.2_TWR-K65F180M\boards\twrk65f180m\usb_examples\usb_keyboard2mouse
That demo works as expected.
Below is my test hardware platform:

I also attached the test result with attached video file.
Please check you are using TWR-SER board as USB FS connector. And the TWR-K65F180M R189 and R190 using 0ohm resistor at side A, not side B.
If K65 FS USB as USB host, the TWR-SER board jumper setting J10 1-2, J16 1-2.
Wish it helps.
Have a great day,
Ma Hui
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