If my opponent is attacking at a battlefield and I stun their 4 might unit against my 3 might unit, what happens?

The attacker's 4 might unit is Recalled, and you Conquer the battlefield.

Here's the breakdown:

1. Combat Damage Step: The stunned 4 might unit contributes 0 damage (Rule 423.1.b). Your 3 might unit contributes 3 damage. You assign that 3 damage to the 4 might unit — not enough to kill it (needs 4 damage to reach lethal).
2. Combat Cleanup: Both units survive the damage step. Since Defenders (your unit) are still present, the Attacker's unit is Recalled to base (Rule 461.1.a.2).
3. Result: You are the only player with units remaining → you Establish Control and Conquer the battlefield (Rule 461.5).