"Water is running into the kitchen."
Translation:Wasser läuft in die Küche.
See philster043's comment above, the accusative (in die Küche) shows that there is movement from outside the kitchen into the kitchen. Ich komme in die Küche means i am outside the kitchen going in. The dative case (in der Küche) shows that it is in the kitchen and stays in the kitchen.
If the question was "water is running in the kitchen", then yes, you'd be correct. Like, you left the kitchen tap running or something. But the question says "water is running into the kitchen", which requires accusative case "in die Küche" to convey motion. It's a weird question because I can't picture a scenario where water is going to be running into a kitchen. Maybe a flood or something?