Can I use both of these interchangeably?
Maybe we had to go through that.
Maybe that's what we had to go through.

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Answer

Hi Sinem, your picture is a perfect representation of those two phrases. Both are correct, but I would tend to add the word 'just' with the meaning of 'just one of those things that happen'  When speaking these phrases, the word 'had' would be emphasised (said a little louder).
 - Maybe we just had to go through that.
- Maybe that's just what we had to go through.

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Yep. They both sound good to me.