Given:
Tap A can fill the tank in 16 hours.
Tap B takes 4 hours more than Tap A to fill the tank.

To find:
The time taken by Tap B alone to fill the entire tank.

Let's solve this step by step:

1. Find the rate of filling of Tap A:
Since Tap A can fill the tank in 16 hours, the rate of filling of Tap A is 1/16 of the tank per hour.

2. Find the rate of filling of Tap B:
Tap B takes 4 hours more than Tap A to fill the tank. So, it takes a total of 16 + 4 = 20 hours for Tap B to fill the tank.
Therefore, the rate of filling of Tap B is 1/20 of the tank per hour.

3. Find the combined rate of filling of Tap A and Tap B:
When both the taps are open, their rates of filling are added.
So, the combined rate of filling of Tap A and Tap B is (1/16 + 1/20) of the tank per hour.

4. Find the time taken by Tap B alone:
Now, we need to find the time taken by Tap B alone to fill the entire tank.
Let's assume it takes 'x' hours for Tap B alone to fill the tank.
Therefore, the rate of filling of Tap B alone is 1/x of the tank per hour.

5. Equate the combined rate of filling and the rate of filling of Tap B alone:
We know that the combined rate of filling of Tap A and Tap B is (1/16 + 1/20) of the tank per hour.
So, (1/16 + 1/20) = 1/x.
Simplifying this equation, we get (20 + 16)/(16*20) = 1/x.

6. Solve for x:
To find the value of x, we can cross multiply and solve the equation:
20x + 16x = 16 * 20.
36x = 320.
x = 320/36 = 8.888 hours.

7. Convert the time to minutes:
To find the time taken by Tap B alone in minutes, we multiply the number of hours by 60:
8.888 hours * 60 = 533.333 minutes.

Therefore, Tap B alone requires approximately 533.333 minutes to fill the entire tank.

Rounding off the answer to the nearest whole number, Tap B alone will take 534 minutes to fill the entire tank.

The correct answer given is 384, which seems to be incorrect based on the calculations.