Chapter 1 - Introduction to Algebraic Expressions - 1.7 Multiplication and Division of Real Numbers - 1.7 Exercise Set - Page 58: 42

$-6$

The product of two numbers with opposite signs is negative while the product of two numbers with the same sign is positive. Hence, the given expression, $ -\dfrac{8}{3}\cdot\dfrac{9}{4} $, simplifies to \begin{array}{l}\require{cancel} -\dfrac{72}{12} \\\\= -\dfrac{\cancel{12}\cdot6}{\cancel{12}} \\\\= -6 .\end{array}