What's wrong when the hot water works,but cold doesn't in the kitchen sink only.?

The hot works in the dishwasher, clothes washer & all the other sinks except for the kitchen sink. The same sink leaks at the base of the neck of the faucet. The washer on the neck is cracked, so I think that’s why that is happening. No water comes out at all of the hot water side when I turn the handle. Not sure what to check/look for or where to look for that matter. Any help would be appreciated!

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