we have the compound inequality
6< 5x -9 < 11
step 1
solve
5x -9 < 11
5x < 11+9
5x < 20
x < 4
solution 1 is the interval (-infinite, 4)
step 2
solve
6< 5x -9
6+9 < 5x
15 < 5x
3 < x
rewrite
x >3
solution 2 is the interval (3, infinite)
step 3
the solution of the compound inequality is
(-infinite, 4) ∩ (3, infinite)=(3,4)
the solution in a number line is the shaded area between the numbers 3 (open circle and 4 (open circle)
see the attached figure
