The gravitational force gives rise to centripetal acceleration. Given the distance in part (b), which is greater than the radius of the Earth, we should use Newton's Law of Gravitation instead of ma = mv^2/r (which assumes constant acceleration and doesn't account for reduced acceleration at higher distances.
F = G*m1*m2/r^2 = m1v^2/r where m1 is the satellite mass. This gives us G*m2/r = v^2. From here, you can plug in the Earth's mass and the gravitational constant G as well as the distance r (given in part a and b respectively) to solve for v, and then from there divide the distance (given by the circumference 2*pi*r) by the velocity to get the orbit time.
