The triangle inequality theorem says that the sum of any two sides of a triangle must be bigger than the third side. If we call the missing side x, then the following two inequalities must be true:
x + 6 > 13 (assumes x is not the longest side)
6 + 13 > x (assumes x is the longest side)
Solving those inequalities yields x > 7 and x < 19 so your compound inequality is
7 < x < 19. Notice that it is not greater/less than or equal to; the third side cannot be 7 or 19.
Short cut: add the two sides given to get the larger limit; subtract the two sides given to get the smaller limit. (6+13=19, 13-6=7).
Hope this helps!
