That won't complete the quest; it requires 'fight and win' an encounter.
@Frost Knight
From your pics, you appear to play on the mobile app. Browser play is playing the game on a computer instead. Fighting on the app (especially learning it) is tough. Browser allows you to fight manually instead of only auto fight (that's available, too, on browser, and skips going to the battlefield just like mobile) where you can actually see what the battlefield looks like and you can control your own troop movements/strikes. Also, you can choose to go to the battlefield, hit 'finish automatically' and watch the fight (I learned a lot this way!). This game was browser only for years before they developed a mobile app. ElvenArchitect has been around for years as well, but only works well on browser, it is not mobile-friendly.
Here's a link to a thread about a beginner's perspective on auto-fight that has loads of pics (scroll down) of what the fights look like on browser:
AutoFight from Beginner's Perspective
That said, in your current situation, I'd pick the 2nd battle (with Thief, Bandit, DroneRiders and Orc General), train up a few more Treants, and go in with 2 Golems/3 Treants. Unless there's horrible terrain issues, that should win the battle. Expect to take losses, and I'd expect those losses to be primarily Golems.
Another note: Each enemy is weaker in the 2nd battle because the squad size is spread over 6 troops instead of 5. You'll see some fights with only one enemy unit and the enemy squad size is huge. I've seen those battles won with few losses: 5 Archers v 1 Orc General or 5 Golems v 1 Bandit. That Archers v Orc General battle can be a zero loss battle if the terrain is favorable to your Archers.