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 $\displaystyle \sqrt{4^2 + 2^2 - 2(4)(2)cos(135)} = 5.6\ miles$
Now, to find the direction from which he is from the initial point is obtained using the sine rule.