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I have a layer of the world that contains 200 rows.

I am required to color the map with six selected colors, the rainbow colors.

I figure that I can save selected countries and save them separately.

Once they saved I can upload them and make the color ramp I needed.

However, I was wondered is there a faster way to do this without making six layers and without choosing each country manually in the Layer Styling bar panel.

Following further clarification by Nitzan Matan, this is another map representation.

This categorization was made by round((y(centroid($geometry))+80)/30) .

To divide latitude range (-90 ~ +80) in this sample data from Natural Earth into 6 zones (bands), I first added 80 and divided by 30. You will need to modify these numbers according to your dataset.

Now change the color to fit with your rainbow palette.

NB One caveat - you will notice Alaska is green. If you want it to be like Russia and Canada, consider breaking US into parts.

As you are using QGIS 3.4.2, you can use Topological coloring Tool, which is in the Processing Toolbox | Cartography.

Start this tool and give 6 (any number of colors you want to have) in the Minimum number of colors and hit Run. It will return a new layer Colored with an additional integer field color_id.

So the last step is to open the Layer Property of this layer and set Categorized color scheme on the color_id column (field). You then change each of these 6 random colors to your rainbow palette.