Lines and regions

There is a beautiful formula which gives the maximum number of regions that can be made in a circle:

$\large \dfrac{n^2 + n + 2}{2} \text{ where } n \text{ is the number of lines}$

Inputting $6$ gives us $\color{#20A900} \boxed{22}$

However, if you want it in a diagram; here you are:

With the $k$ th line we can create $k$ new regions by intersecting all the previous lines. Thus the maximal number of regions we can create with $n$ lines is $1+\sum_{k=1}^{n} k = 1+\frac{n(n+1)}{2}$ , since we start out with one region. For $n=6$ this comes out to be $\boxed{22}$ .