Hi Octavi. "At koge" = "To cook, or, to boil". So, I cook/boil the food.
"At lave" = "To make". So, I make the food. However, The Danes generally say "Jeg laver mad", whether they are boiling a soup, roasting a duck, or just buttering a sandwich.
I'm barely into this lesson and got this as a select a word, but 'food' wasn't an option. There's no way to know that Duo uses 'laver mad' as a kind of idiomatic expression for cooking instead of the direct translation of make food.