Use the numbers $480$ and $12$ to calculate brochures per minute. Which operation will give you "per minute"?

Once you know how many brochures are made in 1 minute, multiply that rate by $30$ to find the total for $30$ minutes.

You can also set up a proportion: $\dfrac{480}{12} = \dfrac{x}{30}$, where $x$ is the number of brochures in $30$ minutes, and solve for $x$.

In Desmos, type the expression (480/12)*30 and press Enter. The output value is the number of brochures the machine can produce in 30 minutes at the given rate.

We are told the machine produces $480$ brochures in $12$ minutes.

Compute how many brochures it produces in 1 minute by dividing:

This gives the production rate in brochures per minute.

Now actually do the division:

So, the machine produces $40$ brochures each minute.

If the machine makes $40$ brochures each minute, then in $30$ minutes it makes

So the machine can produce $1{,}200$ brochures in $30$ minutes, which corresponds to answer choice D.