The rate of increase in households living in apartments is higher than that of detached houses.
Literal
Detached-house [than-より] shared-housing [at-に] live households [possessive-の] increase-rate [side-の方が] high.
Uses the comparative より~の方が高い: 'X's rate is higher than Y's.' 一戸建 (detached house) and 共同住宅 (shared/apartment housing) are housing classification terms. 増加率 (rate of increase) is a formal statistical compound. A dry but structurally useful comparative sentence.