Answer:
 a)  Initial speed of the ball = 14.45 m/s
 b) At height 6 m speed of ball = 9.55 m/s
 c) Maximum height reached = 10.65 m 
Explanation:
a)  We have equation of motion  , where s is the displacement, u is the initial velocity, t is the time taken and a is the acceleration.
, where s is the displacement, u is the initial velocity, t is the time taken and a is the acceleration.
 s = 6 m, t = 0.5 seconds, a = acceleration due to gravity value = -9.8
  Substituting
     
  Initial speed of the ball = 14.45 m/s
  b) We have equation of motion  , where v is the final velocity
, where v is the final velocity
    s = 6 m, u = 14.45 m/s, a = -9.8
     Substituting
         
   So at height 6 m speed of ball = 9.55 m/s
c) We have equation of motion  , where v is the final velocity
, where v is the final velocity
    u = 14.45 m/s, v =0 , a = -9.8
    Substituting
      
   Maximum height reached = 10.65 m