"He looks like his mother."
Translation:Han är lik sin mor.
What is wrong is the word honom, the rest is correct. The word to use is either hans or sin depending on if you are more formal/grammatically correct. Sin is the grammatically correct version but while hans is also somewhat correct but it is seen as slightly sloppy grammatically and bit bad Swedish kind of.
I hope my explanation helped you understand what duolingo was after in this task!