I ride successfully along some roads with a posted speed of 100 km/h (65 mph) and there are other roads posted at 50 km/h (35 mph) that I avoid.
The difference is in the shoulder and general condition of the shoulder. In your photo there IS a paved shoulder, compared to some of my roads where the seal stops at the white painted line.
However there's nowhere to go if things go wrong, between the concrete edging blocks and what looks like an elevated roadway.
Personally I would not ride that road as pictured, unless it was literally the only way through.
More specifically you're on the North Nimitz Highway in Honolulu, Hawaii, USA. Also known as "Hawaii Route 92"
It seems that cycling on a Highway or Freeway is illegal in Hawaii (though not completely confirmed) So if you do there could be fines if caught, and given the USA's attitude toward liability, you may be on the hook for any events or accidents where you were involved or even just near.
Upshot - don't ride on highways/freeways. Find a better route.
Bicycles are prohibited on freeways and sidewalks
from https://www.lonelyplanet.com/usa/hawaii/narratives/practical-information/transport/getting-around/bicycle
HOWEVER
Casual browsing around streetview shows this scene
So theres evidence in both directions that "highway" may not mean the same thing to different people.
From comments - Google Maps website has a bicycle map mode, where dedicated bike paths, dedicated lanes and bike-friendly roads are marked. There is a bike path/lane underneath the road.
https://www.google.com/maps/@21.3372594,-157.9196253,15z/data=!5m1!1e3