We are given the equation:

$$
\(\frac{0.00016 \times 10^m}{800 \times 10^{-5}}=0.02 \times 10^{14}\)
$$

and need to find the value of $m$ from the provided options.

Step 1: Simplify the Numerator and Denominator
First, express all numbers in scientific notation to simplify the calculation.

1. Numerator: $\(0.00016 \times 10^m\)$
- $\(0.00016=1.6 \times 10^{-4}\)$
- So, the numerator becomes: $\(1.6 \times 10^{-4} \times 10^m=1.6 \times 10^{m-4}\)$

2. Denominator: $\(800 \times 10^{-5}\)$
- $\(800=8 \times 10^2\)$
- So, the denominator becomes: $\(8 \times 10^2 \times 10^{-5}=8 \times 10^{-3}\)$

Step 2: Rewrite the Equation
Substitute the simplified numerator and denominator back into the equation:

$$
\(\frac{1.6 \times 10^{m-4}}{8 \times 10^{-3}}=0.02 \times 10^{14}\)
$$


Step 3: Simplify the Left Side
Divide the coefficients and subtract the exponents:

$$
\(\frac{1.6}{8} \times 10^{(m-4)-(-3)}=0.2 \times 10^{m-1}\)
$$

- $\(\frac{1.6}{8}=0.2\)$
- $\((m-4)-(-3)=m-1\)$

So, the equation becomes:

$$
\(0.2 \times 10^{m-1}=0.02 \times 10^{14}\)
$$

Step 4: Express Both Sides with the Same Coefficient

Rewrite 0.02 as $\(0.2 \times 10^{-1}\)$ :

$$
\(0.2 \times 10^{m-1}=0.2 \times 10^{-1} \times 10^{14}=0.2 \times 10^{13}\)
$$


Step 5: Solve for $m$
Since the coefficients 0.2 are equal, we can set the exponents equal:

$$
\(\begin{gathered}
10^{m-1}=10^{13} \\
m-1=13 \\
m=14
\end{gathered}\)
$$


Verification
Substitute $m=14$ back into the original equation to verify:

$$
\(\frac{0.00016 \times 10^{14}}{800 \times 10^{-5}}=\frac{1.6 \times 10^{10}}{8 \times 10^{-3}}=0.2 \times 10^{13}=0.02 \times 10^{14}\)
$$


The equation holds true.

Conclusion
The value of $m$ is $\(\mathbf{1 4}\)$.