They both mean the same and neither is really more common than the other. I always say 'half a dozen' myself, but I hear others say 'half dozen'.

Hello XiaoDeng :) Both "A half-dozen" and "half a dozen" are correct. Here are some examples : - Please buy half a dozen eggs - A half-dozen slices of ham is required to make this sandwich - There were only half a dozen people at the conference I hope these help with your understanding :))

Just to add to Warren and Greg's answers, there are some other words that work the same way. For example, you can say "a half hour" or "half an hour." I would say that "a half dozen"/"a half hour" is the more casual form, and "half a dozen"/"half an hour" is more standard. As the others have said, both are common. When in doubt, though, you should use "half [of] a/an," which will always be correct. (For example, you can say you have "half a box" of something, but it would be very unusual to say you have "a half-box" of something.)