**Problem Analysis**

Let's assume the numbers A and B.

Given:
- 5% of A + 4% of B = 2/3 * (6% of A + 8% of B)

We need to find the ratio A:B.

**Solution**

To solve this problem, we'll follow these steps:

1. Write the given equation.
2. Simplify the equation.
3. Solve the equation for A and B.
4. Find the ratio A:B.

**Step 1: Write the given equation**

The given equation is:
5% of A + 4% of B = 2/3 * (6% of A + 8% of B)

**Step 2: Simplify the equation**

Let's simplify the equation step by step.

First, simplify the right-hand side of the equation:
2/3 * (6% of A + 8% of B) = 2/3 * (0.06A + 0.08B) = (2/3) * 0.06A + (2/3) * 0.08B
= 0.04A + 0.05333B (approximately)

Now, substitute this value back into the equation:
5% of A + 4% of B = 0.04A + 0.05333B

**Step 3: Solve the equation for A and B**

To solve the equation, we'll equate the coefficients of A and B on both sides.

Coefficient of A on the left-hand side = 0.05
Coefficient of A on the right-hand side = 0.04

Therefore, 0.05A = 0.04A

Similarly, equating the coefficients of B:
0.04B = 0.05333B

Simplifying these equations, we get:
0.05A - 0.04A = 0
0.01A = 0

0.04B - 0.05333B = 0
-0.01333B = 0

From these equations, we can conclude that:
A = 0
B = 0

**Step 4: Find the ratio A:B**

Since both A and B are 0, the ratio A:B is 0:0.

Therefore, the ratio A:B is 0:0.

**Conclusion**

The ratio A:B is 0:0.