$\text{There are 4 committees, assuming}$ $\color{blue}{a,b,c,d}$.
$\text{Now, each member is in}$ $\color{red}{\text{exactly 2 committees}}$.
$\text{possible combination of 2 committees out of 4 committees will be}$ $\color{violet}{^4C_2 = 6}$ i.e. $\color{maroon}{\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}}$
$\text{And this was also the criteria that}$ $\color{red}{\text{any two committees have exactly one member in common}}$.
$\text{And as we've already seen that the}$ $\color{green}{\text{possible combination of any two committees is 6, then the number of members also be}}$ $\color{orange}{6}$.