Translation:František is looking forward to it like a little child.
Why "František is looking forward to that as a small kid" is not accepted?
Disclaimer: I am learning, too (and this is one person's opinion)!
First, I'd say that "jako" has appeared in the course so far primarily with the meaning of "like" rather than "as," though that may not be a problem.
But to my (US English) ear, "like" just sounds better. "Like a small child" or "like a little kid" sound right, while "as a small kid" sounds... odd. Sort of like part of the sentence is missing -- as if it should be "as a small kid WOULD."
You could try reporting your version if you get this exercise again, though. Maybe "as" was just overlooked.