For quartering large bodies of armed troops among us—declaration of independencethis quote from the declaration of independence most likely refers to which colonial complaint?

The forced housing of soldiers American colonists had to do during and after the French-Indian War (7 years' war). 

Colonists were required under British law to give shelter, feed, and care for British soldiers. This in addition to growing taxes created economic hardship for some colonists. Also British soldiers were famous for being bad guests in the homes of colonists. 

This refers to the issue of the Quartering Act. The colonists felt the idea of being forced to house and feed the soldiers was beyond what they should have to do. Taxes to help pay for troops was one thing, but paying those taxes and having the house soldiers along with it was just too much. They felt this was also an invasion of privacy and that they could no longer freely express themselves in regards to how they were unhappy with the government.