How do I replace a four wire , brown, blue, black,
And red emerson condenser fan motor model
Number k55hxhrd-8822 with a four wire, brown,
Brown/white, black, and white A.O. Smith condenser fan motor model number f48v61ao1

The brown & brown/white will go to the capacitor. The black & white will go to T1 & T2 on the contactor. Did you get a new capacitor when you got the motor? If not, you need to. The motor will be labeled with the correct capacitor to use with that motor.