We need to select 12 trees with at least 2 of each type: hibiscus (H), jacaranda (J), and oleander (O).

First, allocate 2 trees of each type: 2H, 2J, 2O. This uses up 6 trees, leaving 6 more to select.

Consider the following combinations for the remaining 6 trees:

1. 1H, 8J, 2O: Choose 1 more hibiscus, 8 jacarandas, and 2 oleanders. The number of ways is given by: \(\binom{4}{2} \times \binom{9}{8} \times \binom{2}{2} = 54\).
2. 3H, 7J, 2O: Choose 3 hibiscus, 7 jacarandas, and 2 oleanders. The number of ways is given by: \(\binom{4}{3} \times \binom{9}{7} \times \binom{2}{2} = 144\).
3. 4H, 6J, 2O: Choose 4 hibiscus, 6 jacarandas, and 2 oleanders. The number of ways is given by: \(\binom{4}{4} \times \binom{9}{6} \times \binom{2}{2} = 84\).

Summing these possibilities gives the total number of ways: \(54 + 144 + 84 = 282\).