If the $$x$$-intercept of some line $$L$$ is double as that of the line, $$3x + 4y = 12$$ and the $$y$$-intercept of $$L$$ is half as that of the same line, then the slope of $$L$$ is :

First, we need to find the x-intercept and y-intercept of the given reference line $$3x + 4y = 12$$.

To find the x-intercept, set $$y = 0$$ and solve for $$x$$:

$$$ 3x + 4(0) = 12 \implies 3x = 12 \implies x = \frac{12}{3} = 4 $$$

So, the x-intercept of the reference line is 4.

To find the y-intercept, set $$x = 0$$ and solve for $$y$$:

$$$ 3(0) + 4y = 12 \implies 4y = 12 \implies y = \frac{12}{4} = 3 $$$

So, the y-intercept of the reference line is 3.

Now, for line $$L$$, its x-intercept is double that of the reference line. Double of 4 is $$2 \times 4 = 8$$.

The y-intercept of $$L$$ is half that of the reference line. Half of 3 is $$\frac{1}{2} \times 3 = \frac{3}{2}$$.

The equation of a line in intercept form is $$\frac{x}{a} + \frac{y}{b} = 1$$, where $$a$$ is the x-intercept and $$b$$ is the y-intercept. For line $$L$$, $$a = 8$$ and $$b = \frac{3}{2}$$, so the equation is:

$$$ \frac{x}{8} + \frac{y}{\frac{3}{2}} = 1 $$$

Simplify $$\frac{y}{\frac{3}{2}}$$ by multiplying by the reciprocal: $$\frac{y}{\frac{3}{2}} = y \times \frac{2}{3} = \frac{2y}{3}$$. So the equation becomes:

$$$ \frac{x}{8} + \frac{2y}{3} = 1 $$$

To find the slope, we convert this to slope-intercept form $$y = mx + c$$, where $$m$$ is the slope. Solve for $$y$$:

Subtract $$\frac{x}{8}$$ from both sides:

$$$ \frac{2y}{3} = 1 - \frac{x}{8} $$$

Multiply both sides by 3 to eliminate the denominator:

$$$ 2y = 3 \left(1 - \frac{x}{8}\right) $$$

Distribute the 3:

$$$ 2y = 3 \times 1 - 3 \times \frac{x}{8} = 3 - \frac{3x}{8} $$$

Divide both sides by 2:

$$$ y = \frac{1}{2} \left(3 - \frac{3x}{8}\right) = \frac{3}{2} - \frac{3x}{16} $$$

Rewrite as:

$$$ y = -\frac{3}{16}x + \frac{3}{2} $$$

Comparing to $$y = mx + c$$, the slope $$m$$ is $$-\frac{3}{16}$$.

Looking at the options:

A. $$-3$$

B. $$-\frac{3}{8}$$

C. $$-\frac{3}{2}$$

D. $$-\frac{3}{16}$$

The slope $$-\frac{3}{16}$$ matches option D. Hence, the correct answer is Option D.