Well, four hours of direct sun is two hours short of "full sun" by definition. However, it might be enough depending on the quality of light, color of the building -- i.e. reflected light, etc. Is the afternoon shade solid shade from a building or dappled shade from trees? That will make a difference too.
For bush beans, Jade is one variety that has been highly recommended by several forum members including yours truly.
Let's take that for an example. Jade is usually described as matures in 56 days (or some number close to that). This means if you sow the seeds now and they come up right away, you could start harvesting around beginning of September. Bush beans will bear for about two weeks.
I think with the return of normal 60's night temps in NJ, you could probably sow Swiss chard and have them sprout and grow. Swiss chard are good in salads when young and tender, and older big leaves (and stalks) can be used like spinach. Leafy greens don't mind less than full sun. Most people like Bright lights or Rainbow mix with colorful stalks. I have tried another variety called Luculus and that one has lighter colored, more tender leaves, I thought.
Now, even though shorter period of direct sun is thought to be not enough for fruiting vegetables, I just posted [url=https://www.helpfulgardener.com/forum/viewtopic.php?p=266792#266792]photos of my patio garden[/url] and my patio is shaded almost all morning until the sun clears the trees in the back. Then the direct sun shines on it while the sun travels the arc from the trees to the house, then the solid shade of the house slams down. So the tomato/bell pepper corner, particularly, does NOT get anywhere near 6 hours of direct sun.
However, the sun reflects off the windows in the morning, and the rectangle of reflected sun washes over that tomato corner.