1. The problem states that $$\frac{a}{b} = \frac{b}{c} = \frac{c}{d} = k$$ where $$k = 0$$. 2. Since $$k = 0$$, we have: $$\frac{a}{b} = 0 \Rightarrow a = 0$$ (assuming $$b \neq 0$$ to avoid division by zero). Similarly, $$\frac{b}{c} = 0 \Rightarrow b = 0$$ and $$\frac{c}{d} = 0 \Rightarrow c = 0$$. 3. Therefore, $$a = b = c = 0$$. 4. Now, evaluate $$2a + 3b + 4c = 2\times0 + 3\times0 + 4\times0 = 0$$. 5. Hence, the value of $$2a + 3b + 4c$$ is $$0$$.