8:31a When a man sins against his neighbor and is required to take an oath,

“Someone may do wrong to another person. This other person may require/demand that he swear/make an oath ⌊about what he did⌋.
-or-
“An Israelite may harm/injure his fellow Israelite. He must then swear an oath ⌊that it was a mistake/accident⌋.

8:31b and he comes to take an oath before Your altar in this temple,

Then he should come before your (sing) altar in this temple to swear/make/take the oath.
-or-
So he must come to stand before your place for burning sacrifices in this temple. He must promise with an oath ⌊that he is innocent⌋.

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