Given, (a, b) is the midpoint of the line segment joining the points A(10, -6) and B(k, 4)

So, (a, b) = {(10 + k)/2, (-6 + 4)/2}

=> (a, b) = {(10 + k)/2, (-2)/2}

=> (a, b) = {(10 + k)/2, -1}

=> a = (10 + k)/2

and b = -1

Given equation is

a - 2b = 18 ............1

Put value of a and b in equation 1, we get

      (10 + k)/2 - 2(-1) = 18

=> (10 + k)/2 + 2 = 18

=> {(10 + k) + 4}/2 = 18

=> (10 + k) + 4 = 18*2

=> 10 + k + 4 = 36

=> 14 + k = 36

=> k = 36 - 14

=> k = 22

So, the value of k is 22