Position of the object pin to observe parallax

Parallax is observed at most positions. I say most because if you keep the object pin at the center of curvature $(x=2f)$, you will see the image moving with the object pin (no parallax). Also, if you place the object at the focus $(x=f)$, you won't get a clear image. For all other positions of the object pin, you should observe parallax.

Observer shifts his gaze towards the left,the inverted image of pin appears to the right. Then $f<x<2f$.

This statement has 2 pieces of information:

1. The image is inverted
2. When the observer shifts his gaze to the left, the image appears to the right (of the object); this means the image is closer to the observer than the object.

This is enough to deduce the range of $x$; because:

1. When $0<x<f$, image is erect (virtual image) $⇒x≥f$
2. When $x>2f$, image is farther away than the object (real image) $⇒x≤2f$ $$⇒f≤x≤2f$$
3. Since parallax is observed, $x≠f$ & $x≠2f$. $$⇒f<x<2f$$