I have made these multiple rhombi objects, arranged them in a pattern, now I want to save it as a Graphic style so that I can use it as a background, I don't know which process to follow, merely dragging it in the graphic styles panel isn't working, I'm stuck.
You probably don't really mean "style".. all you need is a Pattern Swatch.
Draw a section..
Select that and drag it to the Swatches Panel. This will create a new Pattern Swatch. To refine that swatch, double-click it in the panel...
You can then adjust the tile size and other options. When you're happy click the
Done button at the top of the document window.
Then merely draw any object and click your new Pattern Swatch...
The Adobe Help Files may be of further assistance.