What Faber-Castell Polychromos color codes do I need to paint this?
There are a couple of ways that you can go about matching...

The first is trial and error testing on scrap paper. It's tried and true, really, because all you do is look at the color options in your set and get close, then work with additional blending with other colors to match up. Take notes. :)

The more "scientific" way is to use an application like Photoshop, The GIMP, or similar that you can use to color sample. Use the color sampler tool to get the value of the color and match it up with this chart: http://colour.granjow.net/fabercastell-polychromos.html and test the result on scrap paper.

Bear in mind that in many cases, you're likely to be layering one color over another, so the sampler may not always be accurate. Test and use your own judgement, always, before applying to your art piece. Make sure your scrap paper is the same as the paper you're using for your work.