see, value of $x$ should be multiples of $11$ i.e. $11, 22, 33, ... $
Here, only $66$ and $132$ are the multiples of $11$.
Now, in $66$ minutes, min. needle covers $6^{\circ} * 66 = 396^{\circ}$
$= 360^{\circ} + 36^{\circ}$
$= 36^{\circ}$
hr. needle covers $\dfrac{66}{2}^{\circ} = 33^{\circ} $
distance covered by (min. needle - hr. needle) = $36^{\circ} - 33^{\circ}$ = $3^{\circ}$
so, $66$ minutes can be omitted.
Now, in $132$ minutes, min. needle covers $6^{\circ} * 132 = 792^{\circ}$
$= (360*2) ^{\circ}+ 72^{\circ}$
$= 72^{\circ}$
hr. needle covers $\dfrac{132}{2} ^{\circ}= 66 ^{\circ}$
distance covered by (min. needle - hr. needle) = $72^{\circ} - 66^{\circ}$ = $6^{\circ}$
So, $132$ minutes will be the correct answer.