The Compromise of 1850 included several important provisions regarding the status of slavery in the territories acquired after the Mexican-American War. Here's an accurate description of the terms related to the options you provided:
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All slavery was eliminated in the District of Columbia: This statement is partially true; the Compromise of 1850 did abolish the slave trade (but not slavery itself) in the District of Columbia. Enslaved people could still be held there.
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California was allowed to annex New Mexico, extending slavery into that territory: This statement is incorrect; California was admitted as a free state and did not annex New Mexico.
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Texas was allowed to annex New Mexico, extending slavery into that territory: This statement is also incorrect; Texas did not annex New Mexico, although Texas received financial compensation for its claims to parts of New Mexico.
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Popular sovereignty was established, allowing states to vote on whether or not to have slavery: This statement is accurate; the concept of popular sovereignty was indeed a part of the compromise, allowing the territories of New Mexico and Utah to decide for themselves whether to allow slavery.
In summary, the most accurate statement regarding the Compromise of 1850 from your options is that popular sovereignty was established, allowing states to vote on whether or not to have slavery.
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