1. The problem involves a quadrilateral GFVH inscribed in a circle with given angle measures at points V and H, and an external or arc angle near G of 168°. 2. We are asked to find the arc FV corresponding to the angle at point F (? degrees). 3. In a circle, the measure of an exterior angle of a cyclic quadrilateral is equal to the measure of the intercepted arc opposite the angle. 4. The exterior angle at G is given as 168°, so the arc FV that it intercepts is also 168°. 5. Therefore, the measure of arc FV is $\boxed{168^\circ}$.