Connecting push fit to a 3/8in supply faucet line: NPTF to compression threads?
You will need two fittings to connect 3/8 tubing to 3/8 compression together. Use Teflon tape between the two fittings to prevent leaks, but don't use any on the compression fitting. Remove and discard the brass compression nut and brass compression ring/sleeve to connect your 3/8 hose.

John Guest - Straight Adaptor – Nptf Thread

Part No. PI011223S --- TUBE OD 3/8" --- THREAD NPTF 3/8"

http://www.johnguest.com/product/inch-size-threaded-fittings/straight-adaptor-bsp-thread-3/

BrassCraft - Compression Female Adaptor

Part No. 66-6-6 --- 3/8 in. O.D. Tube x 3/8 in. FIP

https://www.brasscraft.com/product/38-in-o-d-tube-x-38-in-fip-3/