So the theme of this page seems to be “things that Mary can do”.
For number 7, the answer is メアリーさんは車が運転できます。
Isnt this just… wrong? We are obviously supposed to be talking about what Mary can do, not what the car can do.
What am I missing here?
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が can also mean thing being interacted with.
it mentions subject identification particle. Yeah most people would assume it means car, but it’s giving a very descript response, as opposed to something like
メアリーさんは運転出来ます。 can drive what? a boat? a train? someone insane?
It’s similar in english “mary can drive a car” compared to “mary can drive”
The book is being very deliberate and liberal with が and は, almost soley for teaching purposes, so you see how the words interact with each other.
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What i wrote before was kind of irrelevent.
Instead, have an example from another post of a verb that acts the same way:
私は黒板が見えません。
(I can’t see the blackboard).
The subject is the thing that can be seen/visible in the case of 見える, just like the subject is the thing that is doable in the case of できる. I believe they are both intransitive, potential verbs.
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When you want to say “I can speak Japanese” it is “日本語が話せます”.
I think the potential form of verbs is usually used with が instead of を.
In this type of sentence you can think of it not as “I can speak Japanese” but
something like “Japanese is speakable for me”.
In your case it would mean something like “As for Mary, cars are drivable for her”.
Same thing happens for 好き: “Mary likes dogs” … “As for Mary, dogs are likable for her”.
“メアリーさんは犬が好きです”
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It is not a mistake, and you’ll see why reading up on potential verbs in ch. 13:
If you see the example at the bottom of p. 10, it says “私は日本語が話せます”, further explaining that verbs that takes the particle を can take either を or が, while できる (the potential form of する) almost always takes が, and that using を with できる is considered substandard.
So just think that whenever you have a potential verb, it is always safe to replace を with が 
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