6. \( \left(\frac{7}{12} \times \frac{9}{14}\right)+\left(\frac{3}{8}-\frac{6}{8}\right) \)

Let's break this expression down step by step: First, we calculate \( \frac{7}{12} \times \frac{9}{14} \). To multiply these fractions: \[ \frac{7 \times 9}{12 \times 14} = \frac{63}{168} \] Now, let's simplify \( \frac{63}{168} \). The greatest common divisor of 63 and 168 is 21. So, we divide both the numerator and denominator by 21: \[ \frac{63 \div 21}{168 \div 21} = \frac{3}{8} \] Next, we calculate \( \frac{3}{8} - \frac{6}{8} \): \[ \frac{3 - 6}{8} = \frac{-3}{8} \] Now we sum the results of our previous calculations: \[ \frac{3}{8} + \left(-\frac{3}{8}\right) = \frac{3 - 3}{8} = \frac{0}{8} = 0 \] Thus, the final result is: \[ \boxed{0} \]