The gray cap that Na Hee Do (portrayed by Kim Tae Ri) was wearing before Baek Yi Jin (portrayed by Nam Joo Hyuk) kissed her is from the brand EMIS (Every Moment Is Special). The cap is called EMIS F.Name Corduroy Cap (in Gray) and is priced at 42,000 KRW (around 1,785 pesos).
It is available in the main website of EMIS in different colors: gray, red, orange, green, yellow, navy, and black. Additionally, Sandara Park was also seen wearing the red version of the cap.
You can also buy here: (1)