I visited over maximum e-commerce web site but they have a common thing is that the check out page is always in right side of the page. what is the UX logic / mental model / cognitive science behind this? if i want to place it in left hand side, is it will be treated as wrong UX design?
It depends on the language you’re familiar with.
People who write from left to right feel progress as something from left to right; the right represents what’s "after". People who write from right to left have the inverse expectation.
Most of what we put on the right in the Western world is on the left in the Arabic, Japanese, and Chinese ones. For example, iOS puts the "back" button on the right when used in the Arabic language.