When you ask someone what time it is, this is an example of a situation where you enquire about the time.
(third-person singular simple present enquires, present participle enquiring, simple past and past participle enquired)
In the USA, inquire is generally used in place of enquire. Where enquire is used (particularly in the UK), it means a non-official enquiry (such as to ask a question), whereas inquire is used in legal or government context where official transcripts are generated. In the USA, this distinction is not made and inquire is used generally.
Old French enquerre, from en- + querre (“to search, to look for”).