Not that face-punching or stabbing are good solutions to problems, but these are fictional characters in a fantasy universe, so that's how it rolls.
But the point is: I write a lot of action scenes in my books, and I think a lot about how to make them effective. It's a two-part process.
First: the external. What happens, and showing it in a way that has clarity and engagement. This can be a challenge, especially when your characters are facing nameless thugs. There's only so much "this guy and then the other guy and then the third guy" you can do before it gets confusing. One trick I do is have the POV character make their own distinctions of the people they're fighting, and use that it keeping the situation clear. Another aspect is keeping the geography of the fight clear. Who is where, where they can go, how close they are to each other, so on. Juggling that stuff canbe a challenge, but can make the difference between a fun, dynamic fight scene and a confusing, muddled one.
More importantly is the internal: What does your character feel during the fight? Terrified? Exhilarated? Bored? What do they want? What are the stakes of winning or losing the fight? How does continuing the fight cost them? Give thought to all that.
Now: take those elements, shake them up, and let 'er rip. Like this bit from Parliament of Bodies where Satrine is rescuing a boy from a room filled with gang members, four floors up in a building controlled by that gang.
Satrine took a moment to catch her breath, and pushed through the pain to pull little Yetter with her to the stairs.
A doorway in front of her burst open, and Short Hair came out, knives drawn. Satrine glanced behind her, and Hatchets had come out of the apartment she had just come from. Obviously the rooms up here were connected. And it wouldn’t be too long before the rest of them recovered enough to get out here.
“Back to the wall, kid,” she said, drawing out her handstick.
Short Hair and Hatchets both leaped at her at the same time. Short Hair pounced like a cat, knives first, while Hatchets swung in tight circles—not enough space in this hallway to really go wide. Satrine stepped to the side—to keep Yetter between her and the wall—knocking one of Short Hair’s blades with the handstick before pivoting and sweeping the stick at Hatchets’ tight swings.
She caught the handstick against the hatchet handles, below the blades, and pushed hard to throw him off balance into the wall. Short Hair came up with another swipe, which Satrine pulled back from. She could feel the blade pass by as it barely missed the tip of her nose. She kicked at Short Hair’s knee, while bringing the handstick into the girl’s sternum.
Both Short Hair and Hatchets reeled for a moment, and Satrine pushed Yetter toward the stairs. “Run!” He went like a crossbow bolt down the hallway, and Satrine tried to shove past Short Hair to do the same. Instead something yanked at her leg and Satrine fell to the floor.
She flipped herself over to land on her back, just in time to get her handstick up to block the two knives coming at her chest. She tried to pull up her leg, jam a knee into Short Hair’s side, but Face Scar was on the ground with her, holding on to her boot.
Satrine kicked, knocking Face Scar in the nose while holding back Short Hair’s desperate press to bury her knives into Satrine’s heart. Satrine kicked again, and this time her leg was free—as her foot had come completely out of her boot. She kicked Face Scar again, pushing the girl into Hatchets, who fell on top of Short Hair’s legs.
That distracted Short Hair enough for Satrine to jerk the knives to the side. Short Hair tried to push harder, but just jammed her knives into the floor. Satrine gave her two quick jabs to the face and scrambled out from under the girl.
She was on her feet at the same time as Hatchets, and he just looked annoyed. Satrine was already bruised and winded, a gash on her arm that she only now noticed, one leg aching and the other one with a bare foot.
He came at her with arms like windmills, hatchets spinning, screaming like he was on fire. It would be bad business for Satrine, but he brought the hatchets down in a predictable rhythm that was easy to block. He was swinging too wide, so Face Scar and Short Hair were stuck behind him. Satrine knocked his hatchet blows away as she stumbled back. Quickly he caught on to what she was doing, and tried to switch up his method. He did a fancy spin that looked impressive, but left his back unguarded. She slammed her handstick into his spine, grabbed his shoulder and hurled him into the wall. Both his hatchets got stuck in the wall.
She wasted no more time getting to the stairs, even though she she could only hobble on her uneven feet.
“Someone get that lousy stick!” she heard screamed from behind. As she tried to catch up to Yetter, she could hear plenty of bruisers giving chase, and even more brawling below her.
