Can I fill cells with different colors?

In my current document I have alternate row colors, but as I keep filling it out, I want to be able to assign a different color for individual cells, not for a whole row. Currently, what I am able to do is to highlight the text in a cell in the color I want, but I do not want to highlight the text. Instead, I want to change the background color in the cell. Is this achievable? Should I remove the alternate color in order for it to work?

The odd thing is that when I am on my iphone, I do not have this issue because I see the cells exactly as I want: the whole cell is filled with the color I want instead of only the text appearing as highlighted.