1. The problem gives a number sequence: $$150, m, 126, 114, 102, n$$ and asks to find the value of $$m - n$$. 2. To solve this, we first identify the pattern in the sequence. The sequence appears to be arithmetic, meaning the difference between consecutive terms is constant. 3. Calculate the differences between known consecutive terms: $$126 - m$$ (unknown), $$114 - 126 = -12$$, $$102 - 114 = -12$$. 4. Since the difference between 126 and 114 is $$-12$$, and between 114 and 102 is also $$-12$$, the common difference $$d = -12$$. 5. Using the common difference, find $$m$$: $$m = 150 + d = 150 - 12 = 138$$. 6. Find $$n$$ using the common difference: $$n = 102 + d = 102 - 12 = 90$$. 7. Finally, calculate $$m - n$$: $$m - n = 138 - 90 = 48$$. 8. Therefore, the value of $$m - n$$ is 48, which corresponds to option D.