"Do I just... throw one? Do the colors have significance?"

"Why would I have gotten out four if you were supposed to throw one? Yes the colors have significance."

"So... I throw all four of them? Is there a specific order to throw them in?"

"Yes, no."

"Alright, then." Let's try not to miss.

The first two darts land successfully! The third dart misses, striking too far to the left. She picks it up, blushing slightly, and tries again, hitting the map this time. The fourth dart lands without incident.

"Now what?"

Now Summer takes out the two pieces of red and blue string she grabbed while Celene was doing that, sticks the red string along the line formed by the two red darts, and... hmm. 

"These are too parallel. Try again."

Oh. Uh. Ok.

She tries again.

[For reference, results are being randomly generated using a normal distribution]

Summer is NOT going to carefully imagine four points specified in cartesian coordinates in her head a second time to figure out if the intersection point is reasonably nearby you're gonna have to give the results to her in a format other than metafictional psychic beam if you want her to do something other than arbitrarily posit your attempt to have succeeded

Sure that seems fine

Yay! She finishes lining up the red string along the line formed by the red darts and the blue string along the line formed by the blue darts, and then marks down the intersection point.