Connect 1/2" supply line to 3/8" outer diameter faucet line
You need a brass connector. "1/2" female iron pipe" (1/2" FIP) is the size of the female connector on the end of the hose coming out of the sink plate in your picture; "3/8" female compression" is the size of the connector on the end of the hose coming out of the faucet in your picture. You need a 1/2" MIP (male iron pipe) X 3/8" male compression adapter. Super common at any hardware store, er... should I say "ironmonger shop"?