The meter works both ways--it reads positive if electrons are flowing in one direction and negative if they are flowing in the other.
Assume that normally, the electrons flow from the terminal block to the ammeter and then to the solenoid, and that's a positive reading (I may have it backwards, but it doesn't matter for the sake of the argument). If it's wired so the wire goes through the loop left to right, the ammeter shows positive. If I rewire it so it goes through right to left, the ammeter "sees" the electrons moving the other way, and will read negative, even though the wire itself still has the electrons moving the same way.
Do you have a clamp-on DC ammeter? (I do--very useful device!) If so, clamp it on a cable with DC current and take a reading. Then unclamp it, flip it over so it's facing the other way, reclamp it and take another reading--it will be negative if the first was positive. This is the same effect.
To paraphrase a common poster here: It's the Law--Faraday's Law and Lenz's Law, working together in this case...
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