Examples
Atl. Oc. 1½ mi S. of Shackleford Banks + 2 mi E of Beaufort Inlet. County Carteret, North Carolina
As always, it helps to look at the actual situation and figure out mentally all of the places where the description could be interpreted to be true.
For this one, one half of where it would be true is in a north-south band as wide as east-west width of the inlet at its center (~0.68 mi), plus the twice the uncertainty in the distance measurement from the description (½ mi). The other half of where it would be true is in a shape like the banks, but wider by the twice the uncertainty in the distance measurement from the description (½ mi). So, basically, we want to find the intersection of a band 1.68 mi wide centered 2 mi E of the center of Beaufort Inlet with a fat Shackleford Banks shape (0.5 mi buffer all around it) displaced 1.5 mi S from where the Banks are located.
Now to calculate it. The longitude of the final point should be calculated by going 2 mi E from the center of the Inlet (34.692926, -76.670739 from Google Maps, more or less), which, according to the georeferencing calculator should be at 34.692926, -76.6356112. The latitude of the final point should be calculated by going 1.5 mi south of the center of the banks at the longitude given above (34.680797, -76.635611 from Google Maps, by my reckoning). So the final point should be at 34.680797, -76.6356112.
The Georeferencing Quick Reference Guide says we should do the calculation Error only calculation using the half the width of the larger path. Here I would compare the east-west width of the center of the inlet and the north-south width of the banks at the longitude -76.6356112. The inlet was ~0.68 mi width, and I estimate the banks are ~0.52 mi wide north to south at -76.6356112, so we use the east-west width of the center of the inlet as the Extent.
Plug in the following to the Georeferencing Calculator, following the "Offsets from two Distinct Paths" example in the Georeferencing Quick Reference Guide:
Calculation type: Error only
Locality type: Offset along Path
Coordinate Source: Google Earth/Maps
Coordinate System: decimal degrees
Latitude: 34.680797
Longitude: -76.6356112
Datum: WGS84
Coordinate Precision: exact
Extent of named place: 0.34
Measurement error: 0
Distance units: mi
Distance precision: 1/2 mi
Final answer:
decimalLatitude: 34.680797
decimalLongitude: -76.6356112
coordinateUncertaintyInMeters: 950
geodeticDatum: WGS84