Let the speed by cycling be $X$ km/h and speed of walking be $Y$ km/h
So, $(1/2)X + (3/2)Y = 19\qquad \to (1)$
And, $X + Y = 26\qquad \to (2)$
Solving (i) & (ii) we get, $X = 20$ and $Y = 6$
Thus, the speed in km/h at which Budhan walk is $6.$
Correct choice: option "D."