He went 4 miles to the west and again went 2 miles to north west. how many miles did he go from the initial point.
If you made a simple sketch, I'm sure you'll see it better. The two different paths he took make two lines, and the total distance he is from his initial point makes a third line. In all, they make a triangle.
Since you know the directions he took, you'll see that the angle between the first two sides is 90 + 45 = 135 degrees.
Then, use the cosine rule to find the length of the last side of the triangle, which gives
Now, to find the direction from which he is from the initial point is obtained using the sine rule.