Solution:

Step 1: Finding the values of 'a' and 'b'
Given, (1,4) and (-1,8) lie on the graph of equation ax + by = 6.

Substituting (1,4) in the equation, we get:
a(1) + b(4) = 6
a + 4b = 6 .......... (1)

Substituting (-1,8) in the equation, we get:
a(-1) + b(8) = 6
- a + 8b = 6 .......... (2)

Solving equation (1) and (2), we get:
a = 2 and b = 1/2

Therefore, the required values of 'a' and 'b' are 2 and 1/2 respectively.

Step 2: Plotting the graph of equation
To plot the graph of the equation ax + by = 6, we need to find at least two points on the line.

Putting x = 0, we get:
ay = 6
y = 6/a

Putting y = 0, we get:
ax = 6
x = 6/b

So, the two points on the line are (0,6/a) and (6/b,0).

Plotting these points on the graph and joining them with a straight line, we get the required graph of the equation ax + by = 6.

Explanation:
In this question, we are given two points (1,4) and (-1,8) that lie on the graph of the equation ax + by = 6. Using these points, we can find the values of 'a' and 'b' by substituting them in the equation. Once we have the values of 'a' and 'b', we can plot the graph of the equation by finding at least two points on the line. We can do this by putting either x or y as zero and finding the corresponding values of the other variable. Once we have two points on the line, we can join them with a straight line to get the required graph.

The Shiwalik ranges are the Himalayas' lowermost and southernmost part. The Shivalik range is located on tectonic plates (Eurasian plate and Indo-Australian plate) which makes it more prone to earthquakes. It mainly lies near the river valleys and along with unconsolidated sediments leads to the soil erosion and landslides in the Shivalik ranges.