Suppose that $N$ newspapers have to be delivered. Since Daniel can do the job in $20$ minutes, he distributes $\frac{N}{20}$ newspapers per minute.
Similarly, Francisco delivers $\frac{N}{30}$ newspapers per minute.
So if they work together as described, they deliver a total of $\frac{N}{20}+\frac{N}{30}$ newspapers per minute. In other words, their combined delivery rate is $\frac{N}{20}+\frac{N}{30}$ newspapers per minute.
Thus the total time that they take is the total number of newspapers to be delivered, divided by their combined rate. This is $\frac{N}{\frac{N}{20}+\frac{N}{30}}.\tag{$1$}$ Now we need to do some algebra. The denominator in the above expression is $\frac{N}{20}+\frac{N}{30}$. Bring this expression to the common denominator $60$. We have $\frac{N}{20}+\frac{N}{30}=\frac{3N}{60}+\frac{2N}{60}=\frac{5N}{60}=\frac{N}{12}$. So the expression $(1)$ simplifies to $\frac{N}{\frac{N}{12}},$ which simplifies to $12$.
Remark: The above calculation has an abstract character. To make it very concrete, decide arbitrarily on the number of newspapers to be delivered. It is convenient to assume there are $60$ papers, because $60$ is divisible by both $20$ and $30$.
If there are $60$ papers to be delivered, then Daniel delivers $60/20$ newspapers per minute, and Francisco delivers $60/30$ newspapers per minute. So their combined delivery rate is $5$ papers per minute. Since there are $60$ papers, it takes $60/5=12$ minutes for the two people to deliver them all.
The first calculation that we made uses the general "$N$" instead of the specific (and possibly wrong) $60$. Apart from that, it is exactly the same as our concrete calculation with $N=60$. It is very useful to go through the calculation with concrete numbers, to see what's really going on.