有難い
ありがたい · arigatai · JLPT N2 · i-adj
grateful
🙏 有難い = to exist + hard: something so rare it's a gift
有 means to exist and 難い means difficult, so 有難い first meant rare, hard to come by. Something that rare is worth thanking for, and the word came to mean grateful. Its polite form gives us arigatou.
有 — hand 𠂇 + moon/meat 月
Originally depicted a hand holding a piece of meat (月 here is the 'meat' radical, not moon), expressing the idea of possessing something. Over time the meaning broadened from 'to hold/possess' to the general sense of 'to have' or 'there is/exists'.