Untap, upkeep.
Mountain.
Send in the whole gang. Blocks -- 6/6 blocks 6/4; flyer blocks flyer; last one blocks rats.
My responses, then, are as follows:
Tap my Forest and Swamp to cast Might of the Nephilim (Target creature gets +2/+2 until EOT for each of its colors.) on my Flame-Kin, paying GB and floating R. He is now 8/6.
Tap both Mountains to add RR (now RRR in my pool). Pump the Flame-Kin for 3, making him 11/6.
Tap my Plains and Island to cast Carom (The next 1 damage that would be dealt to target creature this turn is dealt to another target creature instead. Draw a card.) redirecting a damage from my Flame-Kin to your Vengeance (I don't expect it to help with trample damage, but it will make my dude survive).
Stacking and, presumably, resolving the damage results in all of your creatures dying (for which I take 4 damage). My Equenaut and Rats bite it. My Flame-Kin deals 6 damage to your Vengeance and 5 to you, and survives.
Done. Updated the board accordingly.
Mooseman: 3
Hand: 9 (Swamp)
In play:
(T) Plains
(TT) Mountain
(T) Forest
(T) Simic Growth Chamber (T: Add GU .)
(T) Azorius Signet (1, T: Add WU)
Graveyard: Azorius First-Wing, Aquastrand Spider, Squealing Devil, Silkwing Scout, Stalking Vengeance
RFG:
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Rokapoke: 13
Hand: 7
In play:
(T) Forest * Utopian *
(T) Swamp
(T) Island
(TT) Mountain x2
(T) Plains
Utopia Sprawl (Enchant Forest. As ~ comes into play, choose a COLOR. Whenever enchanted Forest is tapped for mana, its controller adds one RED mana to his mana pool.)
Taste for Mayhem (Enchant creature. Enchanted creature gets +2/+0. Hellbent -- Enchanted creature gets an additional +2/+0 as long as you have no cards in hand.)
(T) Flaring Flame-Kin (6/4; As long as ~ is enchanted, it gets +2/+2, has trample, and has "R: ~ gets +1/+0 until EOT.) * Tasty! *
Graveyard: Cackling Flames, Might of the Nephilim, Carom, Freewind Equenaut, Gobhobbler Rats
RFG: