이든지 after a consonant (무엇이든지) · 든지 after a vowel (누구든지) · short form: (이)든
any-, -ever (누구든지 anyone); or (either … or)
Example
궁금한 게 있으면 언제든지 물어보세요.
If you have any questions, ask me anytime.
Word parts
From 이다 'to be' + -든지 'whether (it is)'.
Good to know
With question words it means 'any-': 누구든지 'anyone', 뭐든지 'anything', 어디든지 'anywhere'. In speech it's often shortened: 뭐든 괜찮아요.