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. The suggestions in BOLD are mine.
“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, tap the gas, and let off again.
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”.
To shift out of 4L, stop the vehicle, shift the transmission to Neutral, shift the transfer case lever to 4H, then the transmission to Drive (if you have an automatic), or First gear (if you have a manual), and continue on.