The phrase "do the top of head" refers to giving an answer or response without much thought or preparation. There are many synonyms for this phrase, including "off the cuff," "spur of the moment," or "impromptu." Other possible phrases include "on the fly," "without prior planning," or "without much consideration." Essentially, these terms all imply that the response given is not carefully thought out or well-prepared, but rather a quick and spontaneous answer. It can be helpful to be able to identify and understand these synonyms, as they may be used in a variety of contexts, from casual conversations to more formal settings.