Question 1086782
On the initial drop it falls 6m
It bounces up to 4m (=(2/3)*6)
It then falls 4m to the ground
It bounces up to (2/3)(4) = {{{ (2/3)^2*6 }}}
—
Adding all this up, with D=distance travelled:

{{{ D = 6 + 2 * sum( (2/3)^n,  n=1, infinity )*6 }}}  

—

{{{ sum( a^n, n=1, infinity ) = a / (1-a) }}}   when |a| < 1
—
{{{ D = 6 + 12 * ((2/3) / (1-(2/3)) )  }}}
{{{ D = 6 + 12 * (2) }}}
—
Ans:  {{{ D = highlight(30m) }}}