The correct answer to this open question is the following.
Although there are no options attached we can say the following.
Explain how the balance of power within the government was threatened by the admission of the state of Missouri into the Union.
What happened was that the admission of Missouri into the Union threatened the balance of power in Congress. Slave states in the South feared that they could be outnumbered in US Congress affecting their economic and political interests. And they saw it as a huge risk. That is why supported the Missouri Compromise of 1820 in which Missouri was admitted as a slave state but Main was admitted at the same time as a free state.
The provisions of the Missouri Compromise in addition to admitting Missouri as a slave state were that Maine was admitted as a free state and slavery was prohibited north of latitude 36o30’.
By the 1820s, the United States had several differences regarding slavery and abolition that made most Americans be polarized. Northerners supported abolitionism and Southerners supported slavery. The distribution of power in the US Congress was also a major issue that generated a lot of problems between the states.
The Missouri Compromise was the best answer Congress had at that moment to maintain the relative stability in the country.