jograki said:
I was thinking that too since we did that with another copper pipe, but for this one with the hose being the one with ridges (not sure what it's called) I didn't think that sharkbites adapters would work? Do you know?
If I had to guess that flexible tubing is fixed onto that valve with a "compression" fitting. I put it in quotes because that's the name of it. It's a VERY standard fitting used in residential and commercial plumbing.
Here are 3 examples, all compression fittings, and can all screw directly onto the same valve despite their different appearance. The seal is made when the nut is tightened down and compresses that ring. In the example on the left, it's all built into the fitting on the end of the tubing.
If your new fixture uses a 3/8" (actually that might be 1/4" as I'm 90% certain the size is based on the inner diameter of the tubing) compression fitting then I will almost guarantee that it will mate up to that valve without any necessary adapter. If you need to step up or down a size, Blue, Orange, Red, or any other hardware store will have what you need.
FYI Compression fittings are designed to seal without any Teflon or putty.