Hi. As per Japan Guide, Motonosumi Shrine is very remote and not accessible by public transportation.
A rental car is most convenient to access Motonosumi Shrine. The nearest rental car outlets can be found in Hagi, Yamaguchi and Shimonoseki. From Hagi, it takes about 60 minutes to reach the shrine by car, while it takes about 90 minutes from either Shin-Yamaguchi Station or Shimonoseki. Paid parking is available beside the shrine.
By train and taxi
Nagato-Furuichi Station is the nearest train station to Motonosumi Shrine. There are no buses from the station going to the shrine, and a taxi ride there takes about 20 minutes and costs around 3000 yen one way.
you can check this link https://www.japan-guide.com/e/e6190.html for your reference. :)