Without a minimum number of packets to each teacher, then you have:
(12, 2, 1) , (10, 4, 1) , (8, 6, 1) , (6, 8, 1) , (4, 10, 1) , (2, 12, 1) , (10, 2, 3) , (8, 4, 3) , (6, 6, 3) , (4, 8, 3) , (2, 10, 3) , (8, 2, 5) , (6, 4, 5) , (4, 6, 5) , (2, 8, 5) , (6, 2, 7) , (4, 4, 7) , (2, 6, 7) , (4, 2, 9) , (2, 4, 9) , (2, 2, 11) , (12, 1, 2) , (10, 3, 2) , (8, 5, 2) , (6, 7, 2) , (4, 9, 2) , (2, 11, 2) , (10, 1, 4) , (8, 3, 4) , (6, 5, 4) , (4, 7, 4) , (2, 9, 4) , (8, 1, 6) , (6, 3, 6) , (4, 5, 6) , (2, 7, 6) , (6, 1, 8) , (4, 3, 8) , (2, 5, 8) , (4, 1, 10) , (2, 3, 10) , (2, 1, 12) , (11, 2, 2) , (9, 4, 2) , (7, 6, 2) , (5, 8, 2) , (3, 10, 2) , (1, 12, 2) , (9, 2, 4) , (7, 4, 4) , (5, 6, 4) , (3, 8, 4) , (1, 10, 4) , (7, 2, 6) , (5, 4, 6) , (3, 6, 6) , (1, 8, 6) , (5, 2, 8) , (3, 4, 8) , (1, 6, 8) , (3, 2, 10) , (1, 4, 10) , (1, 2, 12)==63 different ways
Note: The sum of each permutation ==15 and each permutation consists of: Two EVEN numbers + one ODD number.