[RT OSK]

$\Delta ABC \sim \Delta DEF$
$AB // DE$

$\Delta OAB \sim \Delta ODE$
$AB = \frac{1}{2} \times DE = 2$

$\Delta ABC \sim \Delta DEF$
$DE = 2 \times AC = 6$

$\Delta DEF \sim \Delta GEH$
$GH = \frac{DF}{4} \times (4+2) = 9$