backen
to bake
To cook foods such as bread, cake, cookies, or pizza with dry heat in an oven.
Ich liebe den Geruch, wenn meine Oma frisches Brot backt.
I love the smell when my grandma bakes fresh bread.

to bake
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to bake
To cook foods such as bread, cake, cookies, or pizza with dry heat in an oven.
Ich liebe den Geruch, wenn meine Oma frisches Brot backt.
I love the smell when my grandma bakes fresh bread.

'Backen' (to bake) has two past-tense forms. The strong form ('er buk', 'hat gebacken') is the most common, especially with food. The weak form ('er backte', 'hat gebackt') is rarer, more regional, or used in technical contexts such as 'festbacken' (to stick hard).
Gestern buk ich einen Apfelkuchen.
Yesterday I baked an apple cake.
In the context of food, 'backen' (to bake) is typically combined with 'Kuchen' (cake), 'Brot' (bread), 'Plätzchen' (cookies), or 'Pizza' (pizza).
Am Wochenende backen wir immer frische Brötchen.
On weekends we always bake fresh rolls.
The colloquial expression 'etwas gebacken kriegen' means 'to manage something' or 'to get something done'. It is very often used negatively to express that someone can't manage to do something.
Ich kriege es heute einfach nicht gebacken, mich zu konzentrieren.
I just can't manage to concentrate today.
In the meaning 'to stick hard', 'backen' is often combined with a prefix such as 'fest-' or 'an-'. The verb is then 'festbacken' or 'anbacken' and is separable.
Der Käse ist auf dem Teller festgebacken.
The cheese has stuck hard to the plate.
to manage / create
'schaffen' and 'etwas gebacken kriegen' can both express that you manage to do something or get something done. 'schaffen' is neutral and can be used almost anywhere. 'etwas gebacken kriegen' is a fixed colloquial expression and often sounds slightly critical. It is used especially when something is not working out or when you doubt whether someone will manage it. For a normal successful achievement, you would usually say 'schaffen'; when speaking casually or with some irritation, 'gebacken kriegen' fits.

Er kriegt es einfach nicht gebacken, seine Unterlagen rechtzeitig abzugeben.
He just can't manage to submit his documents on time.
Nach zwei Stunden Arbeit hat Lena die Aufgabe endlich geschafft.
After two hours of work, Lena finally managed to finish the task.