Here's how the factory suggests you shift the transfer case and I've been doing this since these things were new and I worked at the dealership. Quoted from the owner's manual.
"To engage, shift the transfer case lever from 2H to 4H while the vehicle is moving at any legal speed". I let off the gas, throw the lever, and then tap the gas and let off.
4L position: " To engage, slow the vehicle to 2-3 MPH , shift the transmission to Neutral, then shift the transfer lever to the right and pull firmly rearward to 4L".