Just a small example to drop some light on how the cases work:

показать тебя (ACCUSATIVE) to someone = to show you to someone:
Я покажу тебя моим родителям. = I will show you to my parents. I will introduce you to my parents.

показать тебе (DATIVE) something (or someone) = to show something (or someone) to you.
Я покажу тебе моих родителей. = I will show you my parents.

Please note that the word order can vary, it is not important to understand the phrase.

Я покажу тебя моим родителям. = Я покажу моим родителям тебя. - Тебя is a direct object, and моим родителям is an indirect object, regardless of the word order.
Я покажу тебе моих родителей. = Я покажу моих родителей тебе. - Тебе is an indirect object, and моих родителей is a direct object, regardless of the word order.

The direct object here means "what is being shown", and the indirect object "to whom this thing is shown".

The following phrase seems strange a bit, but it is fully understandable in Russian:
Я покажу тебя тебе. or you can arrange it a different way: Я покажу тебе тебя.
It can be used when I am going to show you a picture of yourself taken when you were young, for example.

In English it does not make much sense, I think: I will show you you