Question

How many sets of parallel line segments can you find in a cube?

Answer 1

$ABDCHEFGA$ is a cube.

From the fig,The side $AB$ has $3$ sets of parallel line segments $CD,HE,GF=3$ sets

The side $CD$ has $3$ sets of parallel line segments $AB,HE,GF$ in which $AB\parallel CD$ is repeated.Hence there are $3-1=2$ sets

The side $EH$ has $3$ sets of parallel line segments $AB,CD,GF$ in which $AB\parallel CD$ and $HE\parallel CD$ are repeated.Hence there are $3-2=1$ set.

Horizontally$=3+2+1=6$ sets of parallel line segments can be seen in a cube

Consider the side $AG$ has $3$ sets of parallel line segments $BF,DE,CH=3$ sets

The side $BF$ has $3$ sets of parallel line segments $CH,AG,BF$ in which $BF\parallel AG$ is repeated.Hence there are $3-1=2$ sets

The side $CH$ has $3$ sets of parallel line segments $AG,BF,DE$ in which $CH\parallel AG$ and $DE\parallel BF$ are repeated.Hence there are $3-2=1$ set.

Vertically$=3+2+1=6$ sets of parallel line segments can be seen in a cube

Total sets of parallel line segments can be seen in a cube$=6+6=12$