Two particles are simultaneously thrown from the top of two towers...

${v}_{x} = 8\sqrt{2}m{s}^{- 1} =$ relative velocity along x-axis
$∴ x = \left(22 - 8\sqrt{2}t\right)$
${v}_{y} = 6\sqrt{2}m / s =$ relative velocity along the y-axis
$∴ y = \left(9 - 6\sqrt{2}t\right)$
$r = \sqrt{{x}^{2} + {y}^{2}}$
For minimum $r$,
$\dfrac{dr}{dt} = 0 ⇒ t = \dfrac{23}{10\sqrt{2}}s$

$r = \sqrt{{x}^{2} + {y}^{2}}$

substituting the value of $t$ in $r$, {r}_\min = 6m