Given data:
- Distance travelled upstream = 48 km
- Time taken upstream = 6 hours
- Distance travelled downstream = 44 km
- Time taken downstream = 4 hours

Let's assume the speed of the boat in still water is 'b' km/h and the speed of the stream is 's' km/h.

Speed of the boat upstream = (b - s) km/h
Speed of the boat downstream = (b + s) km/h

To find the speed of the boat in still water, we need to solve the following equations:

Equation 1: Speed = Distance/Time
Equation 2: Distance upstream = Speed upstream * Time upstream
Equation 3: Distance downstream = Speed downstream * Time downstream

Let's solve these equations step by step.

Step 1: Find the speed of the boat upstream

Distance upstream = 48 km
Time upstream = 6 hours

Using Equation 1: Speed upstream = Distance upstream / Time upstream
Speed upstream = 48 km / 6 hours
Speed upstream = 8 km/h

Equation 2: Distance upstream = Speed upstream * Time upstream
48 km = (b - s) km/h * 6 hours
8 km/h * 6 hours = (b - s) km/h * 6 hours
48 km = (b - s) km/h * 6 hours

Step 2: Find the speed of the boat downstream

Distance downstream = 44 km
Time downstream = 4 hours

Using Equation 1: Speed downstream = Distance downstream / Time downstream
Speed downstream = 44 km / 4 hours
Speed downstream = 11 km/h

Equation 3: Distance downstream = Speed downstream * Time downstream
44 km = (b + s) km/h * 4 hours
11 km/h * 4 hours = (b + s) km/h * 4 hours
44 km = (b + s) km/h * 4 hours

Step 3: Solve the equations to find 'b' (speed of the boat in still water)

From Step 1: 48 km = (b - s) km/h * 6 hours
From Step 2: 44 km = (b + s) km/h * 4 hours

We have two equations with two variables (b - s) and (b + s). By solving these equations simultaneously, we can find the value of 'b'.

48 km = (b - s) * 6 hours
44 km = (b + s) * 4 hours

Rearranging the equations:
6b - 6s = 48 (equation 4)
4b + 4s = 44 (equation 5)

Multiplying equation 4 by 2 and adding it to equation 5:
12b - 12s + 4b + 4s = 96 + 44
16b - 8s = 140 (equation 6)

Dividing equation 6 by 4:
4b - 2s = 35 (equation 7)

Solving equations 7 and 5 simultaneously:
4b - 2s = 35
4b + 4s = 44

Subtracting equation 5 from equation 7:
4b - 2s - (4b + 4s