Answer:
Part A) 
Part B) The distance between the y-intercepts is equal to 4 units
Part C) The value of h(x) will always be greater than the value of m(x) for any value of x
Step-by-step explanation:
Part A) What is the value of h(4) -m(16)
we have

For x=4

Find the equation of the line m(x)
Find the slope
take the points
(8,2) and (12,4)
The formula to calculate the slope between two points is equal to

substitute



Find the equation of the line in slope intercept form

we have


substitute

solve for b


therefore

Find m(16)

so

Part B) we know that
The y-intercept is the value of y when the value of x is equal to zero
Find the y-intercept of h(x)
For x=0

Find the y-intercept of m(x)
For x=0

therefore
The distance between the y-intercepts is equal to 2-(-2)=4 units
Part C)
Graph both equations


using a graphing tool
see the attached figure
The value of h(x) will always be greater than the value of m(x) for any value of x