why does γιώτα start with γάμα??
Because the sound /ʝ/ is spelled γι- in modern Greek (or just γ- before a front vowel), and the name if the letter is pronounced /ʝota/. Thus it's spelled γιώτα.
Similarly, "doctor" (ιατρός, three syllables, in Ancient Greek) is γιατρός (two syllables) in Modern Greek, since the pronunciation has changed: the ι- at the beginning is no longer a vowel, forming a separate syllable, but something more similar to the y- sound as in English "yes".
It's not wrong, so you should have reported it.
Please look at these which I've posted on another comment.
If you use the Drop down hints you'll find exactly what's expected as the correct translation.
If you have a problem you should report it.
We have no way of seeing what you wrote.
Please read these hints and instructions you'll find them helpful for all your courses.
TIPS TO HELP YOU LEARN + HOW TO REPORT A PROBLEM
And this for the Greek course https://forum.duolingo.com/topic/936
We have prepared links which we think will help you become familiar with the sounds of the Greek.
The Greek Forum https://forum.duolingo.com/topic/936
Other resources: https://forum.duolingo.com/comment/22040507
what is the difference between ο and ω?
They used to make different sounds in Ancient Greek, which is why they used different letters.
Now it's like ee and ea in English: different spellings reflect what used to be different sounds, but that doesn't help anyone learning the language now.
And like English children have to learn to write "clean and green" (not "cleen and grean"), Greek children have to learn where to write ο and where to write ω, since they are now pronounced completely identically.