Explanation:

To find the value of $m$ that makes the system of equations have no solution, they need to be parallel, which happens when their slopes are the same but the intercepts differ.

- The first equation is $18x-72y+13=0$.

- It can be rewritten as $y=\frac{x}{4}+\frac{13}{72}$.

- The slope here is $\frac{1}{4}$.

- The second equation is $7x-my-17=0$.

- It can be rewritten as $y=\frac{7}{m}x-\frac{17}{m}$.

- The slope here is $\frac{7}{m}$.

- Set the slopes equal: $\frac{1}{4}=\frac{7}{m}$.

- Solve for $m$: $m=28$.

- Option:1 - 28

- $\frac{7}{28}=\frac{1}{4}$

- Thus, makes lines parallel.

- Option:2 - 24

- $\frac{7}{24}\ne \frac{1}{4}$

- Option:3 - 9

- $\frac{7}{9}\ne \frac{1}{4}$

- Option:4 - 12

- $\frac{7}{12}\ne \frac{1}{4}$