If the sum of three consecutive even numbers is $78$, what is the second largest number?

Let the three consecutive even numbers be $x$, $x+2$, and $x+4$.
Here, the numbers arranged in ascending order are:

* Smallest number = $x$
* Second largest (or middle) number = $x+2$
* Largest number = $x+4$

Step 1: Set up the equation according to the problem

$$x+(x+2)+(x+4)=78$$

$$3x+6=78$$

$$3x=78-6$$

$$3x=72$$

$$x=\frac{72}{3}=24$$

Step 2: Find the second largest number

$$\text{Second largest number}=x+2=24+2=26$$