I believe it's just off of UT 24 between Green River and Hanksville. The road sign is not on the paved road, it's on the dirt road that leads to the Hans Flat ranger station. 46 miles sounds about right for the road from UT-24 to Hans Flat Ranger Station.
On Google Maps the road shows up as "Lower San Rafael Road." Approximate location would be 38.623208, -110.570965.