To simplify the given expression step by step:

Step 1: Solve the division in the parentheses first.
(-2.4/9 - 1.2/3) = -0.2666666667 - 0.4 = -0.6666666667

(2.5/8 - 3.1/6) = 0.3125 - 0.5166666667 = -0.2041666667

Step 2: Simplify the expression further by substituting the values calculated in step 1.
(3.1/6 + (-0.6666666667)(-0.2041666667) - (1.85 - 4.4) - 5.1/24)

Step 3: Perform the multiplication and subtraction in the expression.
(0.5166666667 + 0.1354166667 - (-2.55) - 0.2125)

(0.5166666667 + 0.1354166667 + 2.55 - 0.2125)

3.4015833334

Therefore, 3.1/6 + (-2.4/9 - 1.2/3)(2.5/8 - 3.1/6) - (1.85 - 4.4) - 5.1/24 is equal to 3.40158.