Assuming that what you want to do is make the small light green polygons be part of the dark green area, and make the small dark green polygons be par of the light green area, you need to use the eliminate tool.
The easiest way to do this is to select all the small polygons what you want to get rid of, and then run the eliminate tool. The tool will only be applied to the selected data.
However, to me it looks like you might need to do some data cleaning first as it looks like you might have some self-intersections in your data.
So your first step is to correct any self intersections you might have. Using a tool like the cut polygon tool should make this process fairly quick for you.
You then need to make sure that your small polygons are individual features, rather than multipolygons. You can do this using the multipart to singlepart tool.
The final step is to then use the eliminate tool as I mentioned above.