You need a hose release tool that can be brought a most auto parts. put on at end of hose connection and pull towards hose, It will go into the fitting and release the tangs that hold it to the barb.
That is called a quick disconnect fitting and it requires a SPECIAL tool to get it loose.
The heater inlet hose is on the firewall. On the 2002 Silverado it is close to the bottom of the firewall on the passenger side.
disconnect the hose and remove 2 bolts.
Quick disconnect. You can get the replacement part that is in the intake at Autozone. If you dont want to do that you cat replace the fitting with a old style one and cut the end of the hose of and slide it on.
The Chevy heater hose removal tool is a plastic piece that clamps around the hose. The tool slides into the fitting to release the hose.
There are many on the engine
I have used a large e-z out extractor tool(same size as fitting)as this is a common problem with GM. products.
removal of heater hose from engine to fire wall
Cool the heater hose and then gently take it off
Want to sea foam my 2002 Chevy 2500hd 6.0 what vacuum hose do I use
It is the heater core hose.
Generally, the upper heater hose leads to the water pump.