To solve this expression, we will first simplify each fraction:

-2/15 = -4/30
1 7/12 = 19/12
2:2 = 2

Now we can substitute these simplified fractions back into the expression and solve:

((-4/30 - 19/12) 30/103) + 2 - 1/4 (9/32)

((-4/30 - 19/12) 30/103) + 2 - 1/4 (9/32)
=(-4/30 - 57/30) 30/103 + 2 - 1/4 9/32
=(-61/30) 30/103 + 2 - 1/4 9/32
=(-61) / 103 + 2 - 9 / 128
=-61/103 + 2 - 9/128
=(-61128)/(103128) + 2 - 9/128
= -7808/13264 + 2 - 9/128
= -7808/13264 + 2 - 9/128
= -7808 + 2 - 82/91
= -7806 + 2 - 82/91
= -7804 - 82/91
= -7804 - 82/91

Therefore, the solution is approximately -7804.9011.