A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

step 1: break each of the three vectors into horizontal + vertical components.
step 2: combine all the vertical components and all the horizontal components
step 3: create a triangle using the vertical and horizontal component
step 4: the hypotenuse of the triangle gives you the distance. you can get the angle using that as well

I tried putting the components together like this
4cos0= 4i
4sin0= 0j
2cos90=0i
2sin90= 2j
1cos30= .86
-1cos30= -0.5

Then I added all the components of (i) and got 4.86i
added all the components of (j) and got 1.5j
used Pythagorean theorem and got an answer of 5.086

I did this but still cant up with right answer... did i do something wrong here?

Yes. The second shot is to the northeast, which means a 45 degree angle, not 90. You calculated a 2 meter shot directly to the east.
The third shot is to the south-west, with means both i and j should be negative.