The problem in the image is asking for the value of the expression:

$\frac{3 \cdot 2^{-1}}{6 \cdot 2^{-3}}$

Let's simplify this step by step:

1. Simplify the numerator and the denominator:

   • Numerator: $3 \cdot 2^{-1} = \frac{3}{2}$ because $2^{-1} = \frac{1}{2}$.
   • Denominator: $6 \cdot 2^{-3} = 6 \cdot \frac{1}{8} = \frac{6}{8} = \frac{3}{4}$.

2. Now, simplify the overall fraction:

$\frac{\frac{3}{2}}{\frac{3}{4}} = \frac{3}{2} \times \frac{4}{3} = \frac{12}{6} = 2.$

Upon reviewing the choices provided (0, 1/2, 1/4), none of these match the correct value of 2, which suggests the problem may have an error or there are additional considerations needed.

Would you like more details on this calculation, or do you have any questions?

Here are some related questions to explore further:

1. What happens if we encounter negative exponents in complex fractions?
2. How can properties of exponents help simplify similar expressions?
3. How do we handle simplifications when both numerator and denominator have common factors?
4. What role do parentheses play in the order of operations for such expressions?
5. How would changing one of the exponents in the original problem alter the solution?

Tip: Always simplify exponents before multiplying or dividing to reduce errors and make calculations easier!