The difference between the German words mehrere & etliche is easy: The word mehrere simply means multiple in English (Notice by the way that it does not mean many - that would be viele). The word etliche, on the other hand means countless or a number of - you would use etliche to express that something has happened very many times - if that makes sense.
German can be a difficult language to learn and comprehend, and oftentimes the smallest words can be tricky to get a handle on. This is especially true with the words mehrere and etliche, which may look and sound similar but have very different meanings.
Let's look at both words in turn!
In German, mehrere is a plural indefinite pronoun meaning "several" or "many". It is usually used when referring to a number of people or things, and can be translated to English as "many", "several", or "a lot of".
Etliche is another plural indefinite pronoun that is used to refer to a number of people or things. However, unlike mehrere, this word has a slightly less definite meaning.
It can be translated to English as "several", "various", or "quite a few". It also has a slightly stronger emphasis on quantity than "mehrere".