What is the minimum land (island) required to support 6 person and enough animals for them.
A lot. Let's assume a temperate climate, not tropical. The equivalent of, let's say, Boston, Mass. 40 to 50 inches of rain per year, and 5 months of winter (you can pretty reliably expect snow to fall, with subfreezing temperatures).
During the 70's the consensus was that, for homesteading, about 5 acres was the minimum for sustainable self-sufficiency for a family of 4. So 6 people, all adults, would need about 10 to 20 acres, more or less. A good part of this requirement is for a woodlot, since you'll need to burn wood for cooking and heating. And if you want to raise something bigger than chickens, you'll need more land for grazing. And if you want draft animals so you can plow with them rather than have your people doing it, that's even more land to support them. For this sort of climate, you should figure on 4-5 acres per animal (horse or cow). The Irish, for instance, got by on less, but Ireland doesn't have freezing winters.
Now, that is in part a conservative estimate. If you want to go the Irish Peasant route, living almost exclusively on potatoes and buttermilk, you'll need on the order of 1 acre. Food ration is about 8 to 10 pounds per day - and nothing else. And, of course, the woodlot needs to be considered. Although the numbers are not well-established, I've run across figures of ~ 1 cord/acre (+/-) for coppiced land. So 5 to 10 acres seems a reasonable estimate.
A more serious problem is water. 10 acres is simply not enough to support decent surface water. After all, you can't dig wells in an oceanic island for water. You need enough land and vegetation to act as buffer and support both the area and relief needed to provide a water source. Frankly, I'm not competent to provide an answer to this aspect, but I'd be very surprised if anything less than 100 acres would work, and I'd be inclined to go for more.
On the other hand, since this is an oceanic island, fishing will presumably provide a fair amount of food, and this will reduce the agricultural requirements.
Enough to have agriculture need and solar panel or other necessary things for the rest of life. solar energy what ever....
And now we start running into trouble. Just exactly what standard of living are suggesting? Solar panels indicate either that the inhabitants won't be there for all that long (it's really hard to make solar panels after all, so they will wear out), or that they will expect to trade with an outside source for goodies like solar panels. In that case, they will need to provide excess produce in order to get their goodies, and the better their standard of living, the more they'll need to produce and the farther away from self-sufficient living they will be.