Teach me to find the value of m and k

First, find the invers of h(x)
h(x) = 4x + m
y = 4x + m
4x + m = y
4x = y - m
x = (y-m)/4
change to function format
h⁻¹(x) = (x-m)/4

We know that the invers of h is
h⁻¹(x) = (x - m) / 4
h⁻¹(x) = x/4 - m/4
The function above should be written similar with the format of
h⁻¹(x) = 2kx + 5/8

Now compare
2kx + 5/8 = x/4 - m/4
change the denominator of right side to 8
2kx + 5/8 = 2x/8 - 2m/8

From the equation above, we find the value of m and k
2k = 2/8
2k = 1/4
k = 1/8

2m = 5
m = 5/2

Final answer
k = 1/8
m = 5/2

How am i goonna know explain