Can you cast a commander from the command zone if it was countered and placed there?

In the Commander format, the command zone is a special zone where your commander can reside and be cast from. The rules specify that whenever your commander would move to your hand, library, graveyard, or exile, you may instead place it in the command zone (or it can go there directly in some cases). This replacement effect applies regardless of the reason the commander is leaving the stack or battlefield.

When a spell is countered, it moves from the stack to its owner's graveyard (CR 701.5a). However, the Commander rules (CR 903.9) provide a replacement effect: if your commander would go to the graveyard or exile from anywhere — including being countered off the stack — you may put it into the command zone instead. This is a replacement effect that applies at the moment of the move.

Once your commander is sitting in the command zone, CR 903.8 allows you to cast it from there at any time you could normally cast it, paying its mana cost plus an additional {2} for each previous time it has been cast from the command zone this game (the 'commander tax').

Concrete example: You cast Atraxa, Praeteors' Voice from the command zone. Your opponent casts Counterspell, countering it. Instead of going to the graveyard, you place Atraxa back in the command zone. On a future turn, you may cast Atraxa again, but now must pay her mana cost plus {2} (the commander tax for the second casting).

There is no restriction on how the commander arrived in the command zone — being countered, dying, being exiled, or starting the game there all lead to the same result: it is castable from the command zone on a future turn.