Translation:Our father had made pizza yesterday.
are they just two different forms?
Correct. There is another variation: εχθές or εχτές. Also, ψες/εψές (local idiom).
And if so, which one is more frequently used?
I don't think either of the χθες/χτες pair is favoured in everyday speech. If we are talking about more formal situations (including written Greek in news outlets for example), I would expect to see the -θ- variations.
There is also οχτώ/οκτώ, εφτά/επτά and others. I think these variations stem from pronunciation and regional accents as the language evolved. In the meantime, as rules were put into place that defined the 'official' language, some forms, either old or new, must have gained popularity while other maintained their local character and are used to the day.
I understand that the word "had" is in there. However, in English, the translation is past perfect, and we only use that form to show an action was completed before a past simple action in the past. "I had eaten before he asked me out to dinner." Thus, I'm not sure if the grammar of the translation is correct although it is a more literal translation.
Since there is so little context, characteristic of many Duolingo sentences, there could easily be an implied context that would warrant the past perfect.
"Our father had made pizza yesterday so he wasn't up to making lasagna. "
We are trying to teach vocabulary and grammar while adhering to Duolingo regulations.
"Είχε μαγειρέψει" does mean had cooked
But in normal idiomatic English what we use for this expression is....""Our father had made pizza yesterday".
You could also have translated it to:
"Our father had cooked pizza yesterday". or "Our father had baked pizza yesterday." which are both accepted translations...but they are not normal English expressions.
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"had made" is Past perfect and it's used to show a "completed action in the past." There is usually some context to determine if you must indicate that it was a completed action. For example I give this to my students:
"After I had closed the door I remembered that I hadn't taken my keys. So, now I had no way to get in again."
After I closed the door I remembered that I hadn't taken my key. But no problem I have another one at the office."
And let's not forget that this exercise if found in the "Past Perfect" Skill so it's what is being taught and of course should be used correctly. Translating means to show what is written. When you are using the language on your own you can use any expression that sounds best to you. Right now learn the vocabulary and the grammar it will come in handy.