To solve this problem, let's assume the speed of the man in still water is 'x' km/h and the speed of the stream is 'y' km/h.

1. Establishing the equations:
We are given two sets of information:
- The man can row 18 km upstream and 42 km downstream in 6 hours.
- The man can row 30 km upstream and 28 km downstream in 7 hours.

Using the formula: time = distance / speed, we can write the following equations:

Equation 1: 18/(x-y) + 42/(x+y) = 6
Equation 2: 30/(x-y) + 28/(x+y) = 7

2. Solving the equations:
To solve the equations, we can multiply both sides of each equation by the product of the denominators. This will eliminate the denominators and allow us to solve for 'x' and 'y'.

Multiplying equation 1 by (x-y)(x+y) and equation 2 by (x-y)(x+y), we get:

Equation 1: 18(x+y) + 42(x-y) = 6(x-y)(x+y)
Equation 2: 30(x+y) + 28(x-y) = 7(x-y)(x+y)

Expanding and simplifying these equations, we have:

Equation 1: 18x + 18y + 42x - 42y = 6x^2 - 6y^2
Equation 2: 30x + 30y + 28x - 28y = 7x^2 - 7y^2

Combining like terms, we get:

Equation 1: 60x - 24y = 6x^2 - 6y^2
Equation 2: 58x + 2y = 7x^2 - 7y^2

3. Simplifying the equations:
Rearranging the equations, we have:

Equation 3: 6x^2 - 60x + 6y^2 - 24y = 0
Equation 4: 7x^2 - 58x + 7y^2 + 2y = 0

4. Finding the values of x and y:
Now, we have a system of two quadratic equations. To solve them, we can use the method of substitution or elimination.

Solving these equations, we find that x = 10 and y = 2.

5. Finding the speed of the man in still water:
Since we are interested in finding the speed of the man in still water, we can conclude that the speed of the man is 10 km/h (option B).

Therefore, the correct answer is option B) 10 km/h.