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The problem provided appears to contain the following equations and conditions:

- \( A = \left( \frac{2^{x+7} \cdot d}{a \cdot 4^{x-3}} \right) \)
- \( B = \left( \frac{b}{2^x} \cdot \frac{54}{c} \right) \)
- Given: \( B = A \) and \( c \cdot b = d \)
  
The task is to solve for \( 2a = ? \).

Let's work through the steps to find \( 2a \). We'll first equate \( A \) and \( B \) and use the given condition \( c \cdot b = d \).

1. Start with the equality \( B = A \):
   \[
   \frac{b}{2^x} \cdot \frac{54}{c} = \frac{2^{x+7} \cdot d}{a \cdot 4^{x-3}}
   \]
   
2. Replace \( d \) using \( d = c \cdot b \), so the equation becomes:
   \[
   \frac{b}{2^x} \cdot \frac{54}{c} = \frac{2^{x+7} \cdot (c \cdot b)}{a \cdot 4^{x-3}}
   \]
   
3. Cancel out the common terms \( b \) on both sides:
   \[
   \frac{54}{2^x \cdot c} = \frac{2^{x+7} \cdot c}{a \cdot 4^{x-3}}
   \]

4. Now simplify \( 4^{x-3} = (2^2)^{x-3} = 2^{2x-6} \), giving:
   \[
   \frac{54}{2^x \cdot c} = \frac{2^{x+7} \cdot c}{a \cdot 2^{2x-6}}
   \]

5. Simplify further by combining powers of 2:
   \[
   \frac{54}{2^x \cdot c} = \frac{2^{x+7} \cdot c}{a \cdot 2^{2x-6}} = \frac{2^{13-x} \cdot c}{a}
   \]

6. Equating the left and right-hand sides:
   \[
   \frac{54}{2^x \cdot c} = \frac{2^{13-x} \cdot c}{a}
   \]

7. Cross multiply:
   \[
   54 \cdot a = 2^x \cdot c \cdot 2^{13-x} \cdot c
   \]

8. Simplify to:
   \[
   54 \cdot a = 2^{13} \cdot c^2
   \]

9. Solve for \( a \):
   \[
   a = \frac{2^{13} \cdot c^2}{54}
   \]

Now, we need to find \( 2a \):

\[
2a = \frac{2^{14} \cdot c^2}{54}
\]

Next, we can evaluate \( 2^{14} = 16384 \), so:

\[
2a = \frac{16384 \cdot c^2}{54}
\]

Given the possible choices, we can try assuming that \( c = 3 \), which simplifies to:

\[
2a = \frac{16384 \cdot 9}{54} = \frac{147456}{54} = 2736
\]

This doesn't match the answer choices directly, so it seems we might need to use a different assumption for \( c \). I'll recheck and simplify based on the choices next. Would you like further clarification or details on the next steps? Here are some follow-up questions:

1. How do we simplify powers of 2 in this problem?
2. What impact does canceling common factors have on solving equations?
3. Can we verify \( d = c \cdot b \) through substitution more efficiently?
4. How can you test the possible values of \( c \) to match the options?
5. What are the strategies for working with equations involving multiple variables?

**Tip:** Always break down equations into simpler forms by isolating common factors or variables.

Jika B = A dan c.b = d dengan A = (2^(x+7) * d / (a * 4^(x-3))) dan B = (b / 2^x * 54 / c) maka 2a = ...

Solve for 2a given the exponential equations involving A = (2^(x+7) * d / (a * 4^(x-3))) and B = (b / 2^x * 54 / c) under the condition that B = A and c.b = d. Learn the steps of simplification, cross-multiplication, and algebraic manipulation to reach the solution.

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