andersherum
the other way around
In the opposite direction, in the reverse way, or in the reverse order.
Du hast dein T-Shirt versehentlich andersherum angezogen.
You accidentally put your T-shirt on the other way around.

the other way around
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the other way around
In the opposite direction, in the reverse way, or in the reverse order.
Du hast dein T-Shirt versehentlich andersherum angezogen.
You accidentally put your T-shirt on the other way around.

The adverb is made up of 'anders' (different/otherwise) and 'herum' (around). It literally means 'around in a different way' or 'turned in the other direction.'
Dreh das Bild mal andersherum, dann sieht man es besser.
Turn the picture the other way around; then you can see it better.
'Andersherum' (the other way around) can stand in position 1 in a sentence to emphasize a statement or introduce a contrast. In this case, the verb follows directly in position 2 (inversion).
Du denkst, ich bin schuld? Andersherum wird ein Schuh draus: Du hast den Fehler gemacht!
You think it's my fault? It's the other way around: you made the mistake!
The literal meaning refers to the physical direction or order of objects. The figurative meaning introduces a new thought or an opposing perspective in a discussion.
Du hast die Batterien andersherum eingelegt, deshalb funktioniert es nicht.
You put the batteries in the other way around; that's why it doesn't work.
on the other hand
'andererseits' and 'andersherum' sound similar, but they have different functions. 'andererseits' is used when you mention a second side or a contrast. 'andersherum' means that something is reversed: in the other direction, in a different order, or from the opposite point of view. Learners may confuse the words because both can express a change in perspective. But 'andererseits' connects arguments, while 'andersherum' turns something around or reverses it.

Du musst das Kabel andersherum einstecken, dann passt es.
You need to plug the cable in the other way around; then it will fit.
Der Plan ist teuer, andererseits spart er später viel Zeit.
The plan is expensive; on the other hand, it will save a lot of time later.