8. \( \frac{7}{9} \cdot \frac{12}{21} \)

First, let's simplify the fractions before multiplying. The fraction \( \frac{12}{21} \) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, \( \frac{12}{21} = \frac{4}{7} \). Now we multiply \( \frac{7}{9} \cdot \frac{4}{7} \). The 7s cancel out, leaving us with \( \frac{4}{9} \). Next, remember to always check for simplification opportunities before performing the multiplication! It not only makes calculations easier, but it often leads to a cleaner final answer. Common mistakes include overlooking these opportunities, which can lead to more complicated fractions than necessary.