Use pathagereom thereom:

Since it is directly north of one house and directly east of the other house, you know that it is a right triangle.

And since the cafe is 2 miles closer to dan than to other person set up equation like this:

a^2 + (a-2)^2 = 10^2

a = 8

Answer C.

You should know the general right triangles to make this problem easier:

6-8-10 (this one would be used for this problem)
3-4-5
And many more....
They should be in any prep company math book

Distance between D to K : 10

Distance between C to D : x-2

Distance between C to K : x

DCK is right angled triangle. Using Pythagoras rule, we get x = 8


(C)