Let's solve the problem step by step.

Let the total capacity of the container be $C$ liters.

1. Initial condition (container is 3/4 full): The amount of water in the container when it is 3/4 full is: $\frac{3}{4} \times C$

2. After removing 6 liters of water (container is 1/2 full): After removing 6 liters, the amount of water left in the container is: $\frac{1}{2} \times C$

According to the problem, when 6 liters is removed, the remaining water in the container equals the amount it would hold if it were half full. Therefore, we can set up the equation: $\frac{3}{4} \times C - 6 = \frac{1}{2} \times C$

Now, let's solve for $C$.

First, subtract $\frac{1}{2} \times C$ from both sides: $\frac{3}{4} \times C - \frac{1}{2} \times C = 6$

To subtract these fractions, let's get a common denominator. The least common denominator between 4 and 2 is 4, so we rewrite $\frac{1}{2}$ as $\frac{2}{4}$: $\frac{3}{4} \times C - \frac{2}{4} \times C = 6$

Now subtract the fractions: $\frac{1}{4} \times C = 6$

Finally, multiply both sides by 4 to solve for $C$: $C = 6 \times 4$ $C = 24$

So, the total capacity of the container is 24 liters.

Would you like more details on any part of the solution or have further questions?

Here are some related questions to explore:

1. What would happen if 12 liters were removed instead of 6 liters?
2. How would the result change if the container started at half full instead of 3/4 full?
3. If the container is 2/3 full, how much water needs to be removed to make it 1/2 full?
4. How do fractions like 1/4, 1/2, and 3/4 represent parts of a whole in real-life scenarios?
5. What is the relationship between fractions and ratios in problems like this?

Tip: When solving problems with fractions, always try to find a common denominator to simplify operations.