I try to find value of $x$ but I can apply none of the following properties for that.
AAS -- Any two angles, and one side (Law of Sines)
SAS -- Side, included Angle, and Side (Law of Cosines)
SSA -- Two sides, and a non-included Angle (Law of Sines)
SSS -- All three sides (Law of Cosines)
Because there are a median, a side and an angle.
How can $x$ value be found?
The left triangle has area $$\frac12 \cdot 8\cdot AD\cdot\sin 30^\circ$$The right one has area $$\frac12\cdot x\cdot AD\cdot\sin 45^\circ$$These two areas are equal, since they have the same base and height.