But I want to play Tic Tac Toe

The image is misleading, all paralle lines are extended indefinitely. A parallelogram is formed from every set of two lines in one direction with every two lines in the other. There are n(n-1)/2 pairs of lines in one, and m(m-1)/2 pairs in the other direction (with n and m the number of lines). This means that there are nm(n-1)(m-1)/4 parallelograms. Here n = 5 and m = 4, yielding 60.

Equation for finding parallelograms when there are m lines intersecting n lines, can be calculated as ${ _{ m }{ C }_{ 2 } }\cdot { _{ n }{ C }_{ 2 } }$ , where ${ _{ n }{ C }_{ r } }$ represents n combination r, or n choose r. Or in another form, $\begin{pmatrix} n \\ r \end{pmatrix}$ or $\frac { n! }{ (n-r)!\cdot r! }$ . Subtitute m and n as 5 and 4, we get 60.

EDIT: The reason why ${ _{ m }{ C }_{ 2 } }\cdot { _{ n }{ C }_{ 2 } }$ works is simple. There are ${ _{ m }{ C }_{ 2 } }$ ways to choose two lines from m lines, and same for n lines. Multiply them, we get this equation.

This one is much more straightforward. There are 5C2 = 10 ways to choose two parallel lines from the set of five. There are 4C2 = 6 ways to choose two parallelograms from a set of four. Any parallelogram is uniquely determined by one pair of lines from the five, and one pair of lines from the four. Thus, the number of possible parallelograms is

(5C2) (4C2) = (10) (6) = 60