Learn German: Hat er die Gabel oder den Löffel genommen?

nehmen (to take) is an irregular, or strong, verb. In the past tense, strong verbs usually start with ge- and end in -en rather than -t. Many also change their core vowel. For nehmen, the 'e' changes to 'o', and the spelling shifts slightly, making it genommen.

The English translation says 'Did he take', but the German says Hat er ... genommen. Why is there no word for 'did'?

German does not use helper words like 'do' or 'did' to form questions. To ask a question about the past, it just uses the normal past tense, which translates literally as 'Has he ... taken?'. The helping verb Hat comes first to make it a question, and the past participle genommen goes to the very end.

Why is it den Löffel instead of der Löffel?

Because the spoon is the direct object of the sentence, meaning it is the thing being taken. Löffel is a masculine noun. In German, when a masculine noun is the direct object (this is called the accusative case), its word for 'the' changes from der to den.

If Löffel changed to den, why did die Gabel stay as die?