Exact answer: 2100pi miles
Approximate answer: 6594 miles
note: I used pi = 3.14 as an approximation. Use more decimal digits for pi if you want a more accurate answer
=======================================
Explanation:
Assume for the sake of simplicity that the satellite travels in a circular orbit. The radius of this orbit is 4000+200 = 4200 miles as we account for the earth's radius plus the height of the satellite. Also assume that the satellite's height doesn't change throughout its orbit.
Find the circumference of a circle with radius r = 4200 miles
C = 2*pi*r
C = 2*pi*4200
C = 8400pi
The satellite travels exactly 8400pi miles in one full orbit around the earth. This takes place over 4 hours. So we can write these three ratios
1 orbit : 8400pi miles traveled
1 orbit : 4 hours
4 hours : 8400pi miles traveled
Now divide both sides of the last ratio by 4 to end up with this...
4 hours : 8400pi miles traveled
4/4 hours: 8400pi/4 miles traveled
1 hour: 2100pi mile traveled
The satellite travels exactly 2100pi miles in 1 hour. This is approximately equal to 2100*3.14 = 6594 miles if you use 3.14 for pi
Use more decimal digits for pi if you need better accuracy