I guess we will have to take this right from the beginning. That's alright though, we've all been here before and it's way better to ask the questions now before you go dig a bunch of dirt that doesn't have any chance of getting you the gold you are prospecting for.
what do you mean by geology?
Geology is the study of the structure of the earth itself. Specifically it is
the science devoted to the study of the Earth, particularly the solid Earth and the rocks that
compose it.
If the type of rocks in your area don't have a form of gold that would end up concentrating in the area you show in your picture there would be no sense in prospecting for gold there.
Gold is pretty rare stuff that isn't found just anywhere. That's part of the reason it's so valuable. If you could find gold just about anywhere it wouldn't be worth much at all.
Once you know some of the basics of geology and the ways gold is concentrated and set free you can study the geology of an area to see if it might be worth prospecting. That's why the geology question comes first.
Luckily most areas already have been studied for their geological makeup so a lot of that preliminary work has already been done for you. If you care to share the location of the area you wish to prospect we might be able to help you with the geology question. A picture really doesn't tell us much about the geology.
not to sure if gold has been found there
The reason I asked this question second is that even if the geological conditions in your area might be right to find gold it doesn't mean that there will be gold there. That's part of the reason gold is so rare. If other people have already found gold in that area then there is a reasonable chance that you too might be able to find gold there.
how do i found out if i can prospect there
If the area might have gold or other valuable minerals there is a good chance that someone else either owns the land or has made a mining claim there. In either of those cases you could not prospect that area without the written permission of the landowner or the person who owns the mining claim. There are other reasons you might not be able to prospect there. You will need to determine the legal status of that portion of land before you can determine if you have a right to prospect there. Once again we would have to know the location of the area in your picture before we can help you determine if you might have the right to prospect there.
Prospecting is an activity that requires knowledge of several different skills. The picture you showed can be a part of figuring out if there is gold there but there are several other things you will have to know before the picture can be of use. There are a lot of people here who can help you develop those skills and help you find your first gold. Give us enough information to get you started and we can help you along the path to being a successful prospector.