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**Hint:**First we will find the slope of the tangent is the differentiation of the given curves with respect to \[x\] and then we will use that for the given equations to coincide, the slope should be equal.

**Complete step-by-step answer:**We are given that the lines \[3x = y - 8\] and \[6x + my + 16 = 0\] coincide.

Rewriting the given equations, we get

\[y = 3x + 8{\text{ ......eq.(1)}}\]

\[y = - \dfrac{6}{m}x - \dfrac{{16}}{m}{\text{ ......eq(2)}}\]

We know that the slope of the tangent is the differentiation of the given curve with respect to \[x\].

Differentiating the equation (1) with respect to \[x\], we get

\[

\Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{d}{{dx}}\left( {3x + 8} \right) \\

\Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{d}{{dx}}3x - \dfrac{d}{{dx}}8 \\

\Rightarrow \dfrac{{dy}}{{dx}} = 3{\text{ ......eq.(3)}} \\

\]

Differentiating the equation (2) with respect to \[x\], we get

\[

\Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{d}{{dx}}\left( { - \dfrac{6}{m}x - \dfrac{{16}}{m}} \right) \\

\Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{d}{{dx}}\left( { - \dfrac{6}{m}x} \right) - \dfrac{d}{{dx}}\left( { - \dfrac{{16}}{m}} \right) \\

\Rightarrow \dfrac{{dy}}{{dx}} = - \dfrac{6}{m}{\text{ ......eq.(4)}} \\

\]

For the given equations to coincide, the slope should be equal.

So, taking equation (3) and equation (4) equal, we get

\[ \Rightarrow 3 = - \dfrac{6}{m}\]

Cross-multiplying the above equation, we get

\[ \Rightarrow 3m = - 6\]

Dividing the above equation by 3 on both sides, we get

\[ \Rightarrow m = - 2\]

**Hence, option B is correct.**

**Note:**The slope equals the rise divided by the run. You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope. Avoid calculation mistakes.

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