In English there's no need for the word "out", as gardens and yards are always outdoors.
I'm not sure why "take the cat TO the garden" is not correct here. It's still the yonelme case, right?
'Take something out ' is same in meaning to 'take out something'
Why not "bahçeden"! Thank you for any explanation.
Because we are taking the cat to the yard. Bahçeden would make sense if we were taking it from the yard (review the distinction between dative and ablative).