To express the phrase "all real numbers that are between -8 and 3" as a compound inequality, you can write:
\[ -8 < x < 3 \]
This means that \( x \) is greater than -8 and less than 3.
To graph the solutions, you would draw a number line, place open circles (or parentheses) at -8 and 3, and shade the area between them to indicate all the values of \( x \) that satisfy the inequality.