Translation:She wants a green hat.
Some colors in Japanese have both a noun and adjective form. Some colors only have a noun form. When you use a noun to describe another noun, you need to use の.
緑色の帽子 (midori iro no boushi) - green hat
赤色の帽子 (aka iro no boushi) - red hat
Many adjectives in Japanese end in -i. When you use an adjective to describe another word, you don't need to add anything. Red has both a noun form and and adjective form, so you can also say red hat this way:
赤い帽子 (akai boushi) - red hat