Translation:I will look the other way while you get dressed.
I wonder if, "I will look away while you get dressed" should be accepted. It's not a literal translation, but it's more natural (and more likely to be said) in English.
I just typed that translation and it was accepted. Thank you to the mods! :)
A slightly easier version might be: Ik zal niet kijken wanneer jij je aankleedt = I won't watch when you get dressed. Zich aankleden (to dress oneself) is a reflexive verb, so you do need jij je in the Dutch sentence.
In English, "the other way" is an adverbial phrase, whereas "the other side" is not. So you can say "I will look the other way" without using a preposition, whereas you cannot say "I will look the other side". Instead, you must say "I will look TO the other side".
In Dutch, "de andere kant" is like "the other side" in English. It needs a preposition or postposition to convert it into an adverbial phrase. Here the preposition/ postposition is "op".
Remember from a previous lesson that Dutch can put the preposition AFTER the noun it modifies to indicate direction. That is, it can use words like "op" as postpositions rather than prepositions.
That is what the "op" is in the Dutch sentence that DL has given us here. I am "looking TO the side" while you get dressed.