Leak under kitchen sink

[majorweenie]

Hello everyone,
I have a leak coming from what seems like that black plastic part under the kitchen sink. I'm not sure what it's called. It seems like it is dripping down the silver and black hose. The black hose goes to my pull out faucet/ sprayer. How would I fix this?

 

[Twowaxhack]

Pull the spout out and make sure the leak isn’t coming from the hose/spout connection.

The hose could have a hole in it.

The on/off cartridge can leak when you’re using it and water can drip down into the cabinet. Take the handle off and operate the faucet and check for leaks there.