Can you say "leftside right"?
Solution 1:
I wish you could - it's just a logical transform of "upside down" and I would understand it. Sadly, many people struggle with left and right, and that coupled with the fact that although some 3D shapes such as boxes definitely have a right and left side, others are more ambiguous (clothing, for example).
It's more common to use "back to front", as in:
"The box was back to front so I fixed it."
or
"I put my trousers on back to front"
There's still the implication of a 180 degrees rotation about the same axis that you describe, but there's no longer the need to figure out left and right.
Solution 2:
No. I'm a native British English speaker and wouldn't have a clue what you meant by "leftside right".
I would suggest describing the action in terms of positioning the faces (left, back, right, front, top, bottom), e.g. "Rotate the box so the left side is facing the front".
Solution 3:
I think "back to front" is what you are looking for, but in my experience as a Canadian, it is not a very common term in American English.
The synonymous term in American English is "backwards". That said, the connotation might be a bit different.
For example, using it the way you used "left-to-right" it may not be a perfect fit. "I turned the box backwards" has some implication that the original position was where it was supposed to be, but I believe most would understand it.
Solution 4:
"180 to the left" is the most natural way I can think of to express it.
In skating/snowboarding, it would be a "backside 180", assuming regular stance ;)