As the feature is on a bearing of 270 relative to the aircraft imagine you are heading due North.

3 minutes later it is at 315, so in effect a 45degree angle.

You are heading North in calm conditions for 3 minutes at 180 knots which equates to a distance of 9Nm.

Imagine your start point which has a side length to the next point of 9Nm, as it was due west at the beginning you have a 90 degree angle and then a 45 degree angle creating a third angle of 45 (as a triangle is 180).

As an isosceles triangle it will have 2 equal sides which are both 9Nm.

The question asks for the minimum distance from the object which is indeed 9. The length of the 3rd side is just over 12!