Yes, you can.
There are many examples throughout the series of successfully Transfiguring animate objects into inanimate objects, so it’s directly shown to be possible - and it’s taught in Transfiguration class beginning in first-year, so it’s not even that difficult.
Which answer in the W.O.M.B.A.T.s should be thought right, then?
It seems answerable by canon information which should be the correct answer to this question. There are examples directly shown in canon for each of these answers choices.
Transfiguring inanimate objects into animate objects is possible.
Before Harry’s first Transfiguration class, Professor McGonagall transfigured her desk into a pig.
“Transfiguration is some of the most complex and dangerous magic you will learn at Hogwarts,’ she said. ‘Anyone messing around in my class will leave and not come back. You have been warned.’
Then she changed her desk into a pig and back again.”
- Harry Potter and the Philosopher's Stone, Chapter 8 (The Potions Master)
Cedric Diggory also Transfigured a rock into a dog.
Transfiguring animate objects into inanimate objects is possible.
Several times in Transfiguration, the students have to turn animals into inanimate objects, starting in first year. One such spell is part of their first-year practical exam.
“Professor McGonagall watched them turn a mouse into a snuff-box – points were given for how pretty the snuff-box was, but taken away if it had whiskers.”
- Harry Potter and the Philosopher's Stone, Chapter 16 (Through the Trapdoor)
There are several more examples, like turning beetles to buttons and hedgehogs to pincushions.
Vanishing inanimate objects is possible.
Bill Weasley vanishes scrolls successfully.
“Bill took out his wand, muttered, ‘Evanesco!’ and the scrolls vanished.”
- Harry Potter and the Order of the Phoenix, Chapter 5 (The Order of the Phoenix)
There are other examples of inanimate objects being vanished, like Snape vanishing Harry’s potions.
Vanishing animate objects is possible.
For their O.W.L.s, the fifth-year students begin learning Vanishing Spells, and first practice on snails.
“By the end of a double period neither he nor Ron had managed to vanish the snails on which they were practising, though Ron said hopefully he thought his looked a bit paler. Hermione, on the other hand, successfully vanished her snail on the third attempt, earning her a ten-point bonus for Gryffindor from Professor McGonagall.”
- Harry Potter and the Order of the Phoenix, Chapter 13 (Detention with Dolores)
Later, they move on to vanishing mice, and Hermione gets good enough where she can vanish kittens.
Therefore, the correct answer should be “None of the above”.
Every example given in the question is shown to be possible to be performed successfully in the books, therefore the only correct answer choice given that accords with what’s shown to be possible is “none of the above”. Why the W.O.M.B.A.T. says it’s a different answer is unclear. It’s possible it was programmed wrong, or the “solved” test made a mistake. However, the answer they say is correct directly goes against canon evidence.
Extra note: “animate objects” is a term indicating something is alive.
The term “animate object” has a known meaning - it refers to something that’s alive and has its own mind, as opposed to an inanimate object.
Linguistics. belonging to a syntactic category or having a semantic feature that is characteristic of words denoting beings regarded as having perception and volition (opposed to inanimate ).
- Animate (Dictionary.com)
It’s listed on several dictionaries as being a grammatical term to distinguish living from nonliving. An example given on one is the word car is inanimate; the word dog is animate. Therefore, it seems very likely that it’s used this way on the test, rather than being used to indicate charmed objects.