Anna throws a ball horizontally off her apartment balcony at a speed of 6.0 meters/second. if the ball falls 10 meters from the balcony to the base of the apartment, calculate how long it takes the ball to reach the base

The horizontal speed is totally irrelevant.  The ball would take the same amount of time to hit the ground if it's tossed horizontally, rolled gently off the balcony, or shot horizontally from a cannon.

The distance it falls vertically is

                      D  =  (1/2) (gravity) (time)² .

                     10m  =  (1/2) (9.8 m/s²) (time²)

                   10m / 4.9 m/s²  =  time²

                     (10/4.9) s²  =  time²

                         time  =  √ (10/4.9  s²)

                                 =      1.43 seconds