To find the percentage increase in the area of a hexagon when all sides are increased by 2%, we can use the formula for the area of a regular hexagon.

Let's assume the original side length of the hexagon is 's'.

Area of a regular hexagon = (3√3/2) * s^2

When all sides are increased by 2%, the new side length becomes (s + 0.02s) = 1.02s.

Therefore, the new area of the hexagon can be calculated as:

New area of hexagon = (3√3/2) * (1.02s)^2

To find the percentage increase in the area, we can calculate the difference between the new and original areas, divide it by the original area, and then multiply by 100.

Let's calculate the percentage increase step by step:

1. Calculate the original area of the hexagon:
Original area = (3√3/2) * s^2

2. Calculate the new area of the hexagon:
New area = (3√3/2) * (1.02s)^2

3. Calculate the difference between the new and original areas:
Difference = New area - Original area

4. Calculate the percentage increase:
Percentage increase = (Difference / Original area) * 100

Now, let's plug in the values and calculate the percentage increase:

Original area = (3√3/2) * s^2
New area = (3√3/2) * (1.02s)^2

Difference = New area - Original area
Difference = (3√3/2) * (1.02s)^2 - (3√3/2) * s^2

Percentage increase = (Difference / Original area) * 100
Percentage increase = ((3√3/2) * (1.02s)^2 - (3√3/2) * s^2) / ((3√3/2) * s^2) * 100

Simplifying the expression:

Percentage increase = ((1.02s)^2 - s^2) / s^2 * 100
Percentage increase = (1.0404s^2 - s^2) / s^2 * 100
Percentage increase = (0.0404s^2) / s^2 * 100
Percentage increase = 0.0404 * 100
Percentage increase = 4.04%

Therefore, the percentage increase in the area of the hexagon is 4.04%. Hence, the correct answer is option B.