Answer
$\text{the interval }\left( 6,12 \right)
$
Work Step by Step
Using the properties of inequalities, then,
\begin{array}{l}
0.3\lt 0.2x-0.9\lt1.5\\
3\lt 2x-9\lt15
\text{...multiply all sides by 10}\\
12\lt 2x\lt24\\
6\lt x\lt12
.\end{array}
Hence, in interval notation form, the solution is $
\text{the interval }\left( 6,12 \right)
$.