This appeared on a motivational poster for teenagers.

Problem:
An apostrophe is required when contracting two words into one word.

Explanation:
“Whether you think you are wrong, …” would be the formal equivalent of what the poster writer wanted to say.

As I’ve written (Did you see the contraction that I just wrote?!), many people often confuse “your” and the contraction of “you are” to the point of writing “your” instead of the contraction.

A contraction requires an apostrophe to signify the removal of one or more letters in the formation of the contraction. For example, the apostrophe in “I’ve” signifies the removal of “ha” in the formation of the contraction from “I” and “have”.

In other words, an apostrophe must appear where one has removed the letter(s) to form the contraction.

Solution:
“Whether you think you’re wrong, …”