Answer
$(-\infty, -18)$
Refer to the attached image for the graph.
Work Step by Step
For easier work, get rid of the fractions by multiplying the LCD of 6 to both sides to have:
$\\6(\frac{1}{3}x +2) \lt 6(\frac{1}{6}x-1)
\\2x+12 \lt x-6$
Subtract $x$ to both sides to have:
$\\2x+12-x \lt x-6-x
\\x+12 \lt -6$
Subtract $12$ to both sides to have:
$\\x+12-12 \lt -6-12
\\x \lt -18$
