Good question! The reason you multiply \(\binom{4}{2}\) and \(\binom{4}{2}\) can be visualized by imagining groups: first, choose the two vertical lines (let's call them A, B, C and D).

M0W2D8-y-choose-horizontal-vertical-lines.png

There are 6 ways to do this:

$$
AB\\\\
AC\\\\
AD\\\\
BC\\\\
BD\\\\
CD\\\\
$$

For each of these 6 ways there are 6 other ways to choose the horizontal lines (let's call them 1, 2, 3 and 4.)

M0W2D8-y-choose-horizontal-vertical-lines2.png

(6 ways starting with AB, 6 ways starting with AD, 6 ways starting with BC, etc.)

AB 12 AC12 AD12 BC12 BD12 CD12

AB 13 AC13 AD13 BC13 BD13 CD13

AB 14 AC14 AD14 BC14 BD14 CD14

AB 23 AC23 AD23 BC23 BD23 CD23

AB 24 AC24 AD24 BC24 BD24 CD24

AB 34 AC34 AD34 BC34 BD34 CD34

There are six groups, with six ways in each group, so that is why there are \(6 \times 6 =36\) ways rather than just \( 6 + 6 = 12\) ways.