Error jumping and moving

Unfortunatly I don't have a solution for you. I have been looking over it for a little bit and don't know what is wrong. I did however clean up the code so it is a little easier to read.

 private Vector3 moveDirection = Vector3.zero;
 private bool grounded = false;
 
 public float speed = 10.0f; 
 public float jumpSpeed = 8.0f; 
 public float gravity = 20f; 
 public int countJump = 0; 
 public int maxJumps = 2;
 
 void OnCollisionEnter()
 { 
     countJump = 0; 
 }
 
 void FixedUpdate () 
     { 
     if(!grounded)
         { 
             moveDirection.x = Input.GetAxis("Horizontal")*speed;
             moveDirection.z = Input.GetAxis("Vertical")*speed; 
         }
     else
         { 
             moveDirection = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));
             countJump = 0;
         } 
         
     if(countJump < maxJumps)
     { 
         if(Input.GetButtonDown("Jump"))
         {
             moveDirection.y = jumpSpeed; countJump ++; 
         } 
     }     
     moveDirection = transform.TransformDirection(moveDirection);
     moveDirection.y -= gravity * Time.deltaTime;
     CharacterController controller = (CharacterController)GetComponent(typeof(CharacterController));
     CollisionFlags flags = controller.Move(moveDirection * Time.deltaTime);
     grounded = (flags & CollisionFlags.CollidedBelow) != 0;
 
     if (Input.GetKey (KeyCode.LeftShift))
     {
         speed = 23.0f;
     }else
     {
         speed = 10.0f;
     } 
 }
 }

The other thing that isn't a big deal but you can use to avoid extra work is using && in an if statement to avoid unnecessary nesting. I am refering to the jump portion of the code where you used:

 if(countJump < maxJumps)
     { 
         if(Input.GetButtonDown("Jump"))
         {
             moveDirection.y = jumpSpeed; countJump ++; 
         } 
     }     

Instead it might be easier to use:

 if(Input.GetButtonDown("Jump") && countJump < maxJumps)
     { 
         moveDirection.y = jumpSpeed; countJump ++; 
     } 

Hopefully someone can answer this for you. If I figure it out I will comeback and respond.

Thanks Go, now works as expected.