Draw a rectangle and label the long sides "6" and label the short sides "x".
The perimeter of this rectangle is now 6+x+6+x = 12 + 2x
The perimeter of a square with side of 4 cm is 4+4+4+4 = 16 cm
We need the perimeter of the rectangle (12 + 2x) to be smaller than (<) the perimeter of the square (16).
Here is the inequality that is needed: 12+2x<16
Solve this (subtract 12 from both sides)
Divide both sides by 2
So the other length your teacher is looking for must be SMALLER than 2 cm.