Chapter 1 - Introduction to Algebraic Expressions - 1.7 Multiplication and Division of Real Numbers - 1.7 Exercise Set - Page 58: 43

$252$

The product of two numbers with opposite signs is negative while the product of two numbers with the same sign is positive. Multiplying the numbers from left-to-right, then the given expression, $ 3\cdot(-7)\cdot(-2)\cdot6 $, simplifies to \begin{array}{l} -21\cdot(-2)\cdot6 \\\\= 42\cdot6 \\\\= 252 .\end{array}