לעכב means "to delay", while להשהות means "to put on hold". "the project was delayed because we didn't get the parts we needed": לעכב "management put the project on hold because it ran out of funds": להשהות (but also לעצור) להשהות isn't used in daily speech, but rather in official announcements, or in the newspaper etc. In daily speech the preferred verb is לעצור.