Mean of the given data is
$\bar{x}=\frac{2+9+9+3+6+9+4}{7}=\frac{42}{7}=6$
The deviations of the respective observations from the mean $\bar{x}$, i.e. $x_{i}-\bar{x}$ are
$2-6,9-6,9-6,3-6,6-6,9-6,4-6$
$\Rightarrow -4,3,3,-3,0,3,-2$
The absolute values of the deviations, i.e. $\left| x_{i}-\bar{x}\right|$ are $4,3,3,3,0,3,2$.
The required mean deviation about the mean is
$MD(\bar{x}) =\frac{\displaystyle \sum_{i=1}^{7}\left |x_{i}-\bar{x}\right|}{7}$
$=\frac{4+3+3+3+0+3+2}{7}$
$=\frac{18}{7}=2.57$