Every time a new line is added, there are as many new regions as the number of lines: With one line there were $2$ regions; with two lines there were $2$ new regions for a total of $2+2 = 4$; with $3$ lines there were $3$ new regions for a total of $2+2+3 = 7$. Continuing this way, when we have $6$ lines there will be $2+2+3+4+5+6 = 22$ regions.