You're right that the correct answer here is wrong (it says "that is a dirty spoon"), but it would be "kijiko kile ni kichafu" since the locative (working as an adjective) would go after the noun, unlike in english.
The given translation is not correct, it says: 'that is a dirty spoon'. Kile kijiko ni kichafu is the correct translation. Kijiko kile = 'that spoon'; Kile kijiko = 'the spoon'.
shouldn't it be "kile ni kijiko kichafu" since it's "that is a dirty spoon" and not "that spoon is dirty"? Also, per my understanding of TZn swahili there are no articles. Though I hear "kile kijiko" a lot I've been taught that it's not correct.