Given $$A = |x + 3| + | x - 2 | - | 2x -8|$$. The maximum value of $$|A|$$ is:

Given equation, $$A = |x + 3| + | x - 2 | - | 2x -8|$$.

Case (i):- $$x+3\ge0,\ x-2\ge\ 0\ \&\ 2x-8\ge\ 0$$

then, $$A = x + 3 +  x - 2  -  2x +8 =9$$.

The maximum value of |A| = 9

Case (ii):- $$x+3\ge0,\ x-2\ge\ 0\ \&\ 2x-8< 0$$

$$x\ge-3,\ x\ge\ 2\ \&\ x<4$$

then $$A = x + 3 + x - 2 + 2x -8 = 4x-7$$.

The range of x is [2,4). Hence the value of A varies from [1,9).

The maximum value of |A| < 9

Case (iii):- $$x+3\ge0,\ x-2 < 0\ \&\ 2x-8< 0$$

$$x\ge-3,\ x < 2\ \&\ x<4$$

then $$A = x + 3 - x + 2 + 2x -8 = 2x-3$$.

The range of x is [-3, 2). Hence the value of A varies from [-9,1).

The maximum value of |A| = 9

Case (iv):- $$x+3 < 0,\ x-2 < 0\ \&\ 2x-8< 0$$

$$x < 3,\ x < 2\ \&\ x<4$$

then $$A = - x - 3 - x + 2 + 2x -8 = -9$$.

The maximum value of |A| = 9

From the above cases, The maximum value of |A| = 9. Option (B) is correct.