To condense the given logarithmic expression $6 \cdot \log_4 2 - \log_4 8$, we'll apply the logarithmic properties:

1. Power Rule: $a \cdot \log_b x = \log_b (x^a)$.
2. Subtraction Rule: $\log_b x - \log_b y = \log_b \left( \frac{x}{y} \right)$.

Step-by-Step Solution:

1. Apply the Power Rule to the first term: $6 \cdot \log_4 2 = \log_4 (2^6) = \log_4 64$

2. Now, rewrite the expression as: $\log_4 64 - \log_4 8$

3. Apply the Subtraction Rule to combine the logarithms: $\log_4 \left( \frac{64}{8} \right) = \log_4 8$

Thus, the condensed form of the logarithmic expression is: $\boxed{\log_4 8}$

Would you like more details on any step? Here are some related questions for further understanding:

1. How does the Power Rule of logarithms work in different contexts?
2. Can logarithms with different bases be simplified?
3. What happens if the arguments of the logarithms are not perfect powers of each other?
4. How would you approach expanding this condensed logarithmic expression?
5. How do logarithmic properties change when dealing with negative terms?

Tip: Always try to express numbers as powers of the logarithm's base to simplify the expression further!