"Showme" is a commonly used term, but there are several other words that can be used in its place, depending on the context. Words such as "demonstrate," "illustrate," "exhibit," "display," and "present" are all appropriate synonyms for "showme."
For example, instead of saying "showme how to change the tire," you can say "demonstrate how to change the tire." Similarly, instead of saying "showme your collection," you can say "exhibit your collection." The use of various synonyms can not only add variety to your language, but also make your expression more precise and clear.