Hola Pati

You can also say "sus colores son azul y blanco". In the exercise we've included the articles because sometimes you can make the colors, that are adjectives, nouns, so we use them with the articles this way (as if we were omitting the word "color": son el [color] azul y el [color] blanco.)

Here's a kwiziq lesson on Spanish adjectives acting as nouns

We'll mark the option without the articles as also correct in this exercise.

Gracias y saludos

Inma