3-3 invasion, stretch, push

https://coinsh.red/ipfs/QmYr6tgtSR7uzot6GZ1qdwdQ8vSqACzQSQBbKW2UDVtdaf

Using MS Paint again, don’t judge

When would I hane (O) as opposed to stretching (X)?

Check out this position in our joseki dictionary.

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(just reposting my answer from Reddit)

Play ‘X’ when you want sente and also are uncomfortable with the situation if White plays ‘B’ or ‘C’ (mainly worry about ‘C’) here

If you’re OK with simply building the wall (I recommend it) then they are pretty similar but ‘O’ should be better and easily manageable.