We have the following inequality:
[tex]|4x-6|<6[/tex]Applying the properties of absolute values we have that:
[tex]\begin{gathered} -6<4x-6<6 \\ \end{gathered}[/tex]Which can be expressed as
[tex]4x-6>-6\text{ and }4x-6<6[/tex]We solve separately and mix the intervals:
[tex]\begin{gathered} 4x-6>-6 \\ x>\frac{-6+6}{4} \\ x>0 \end{gathered}[/tex][tex]\begin{gathered} 4x-6<6 \\ x<\frac{6+6}{4} \\ x<3 \end{gathered}[/tex][tex]0In conclusion, the answer is 0