Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2 - Page 407: 56

$2\sqrt{6}$

Using the properties of radicals, the given expression, $ 7\sqrt{24}-12\sqrt{6} ,$ simplifies to \begin{array}{l}\require{cancel} 7\sqrt{4\cdot6}-12\sqrt{6} \\\\= 7\sqrt{(2)^2\cdot6}-12\sqrt{6} \\\\= 7\cdot2\sqrt{6}-12\sqrt{6} \\\\= 14\sqrt{6}-12\sqrt{6} \\\\= 2\sqrt{6} .\end{array}