One fourth the sum of r and 10 is identical to r minus 4 as a equation

It is important to carefully go through each and every word that is written in the question. Based on the given information's the answer to the question can be easily deduced.
The equation can be written as
1/4[r + 10] = r - 4
r + 10 = 4( r - 4)
r + 10 = 4r - 16
r - 4r = - 16 - 10
- 3r = - 26
Multiplying both sides of the equation by - 1 we get
3r = 26
r = 26/3
  = 8 2/3
So from the above deduction we can conclude that the value of the unknown variable "r" is 8 2/3. I hope the procedure is clear enough for you to understand.

If you would like to write the expression in math, you can do this using the following steps:

one fourth the sum of r and 10 ... 1/4 * (r + 10)
is identical to ... =
r minus 4 ... r - 4

1/4 * (r + 10) = r - 4
1/4 * r + 1/4 * 10 = r - 4
10/4 + 4 = r - 1/4 * r
10/4 + 16/4 = 4/4 * r - 1/4 * r
26/4 = 3/4 * r     /*4/3
r = 26/4 * 4/3
r = 26/3
r = 8 2/3

The correct result would be 8 2/3.