Translate act 2, scene 2, lines 85–127, between Romeo and Juliet into modern-day text messages that you would send via phone, but leave readers able to recognize some of the famous lines from the text.

There are a few ways we can tackle this assignment! One option is to look at each line of Shakespeare's text and directly translate the words and phrases into words and phrases that teens would use today. Another option is to review a summary of the scene and then write your own exchange based on the summary and without directly "translating." This version may end up being shorter, as you will get to the heart of what they are saying, but text messages do tend to be shorter than Shakespeare's lines.
Something else to make your writing stand out is to consider the characterization of Romeo and Juliet. Your task is to turn their lines into text messages, so consider their texting styles. Does Romeo have spelling mistakes in his rush to get his words out? Does Juliet use emojis as symbols for her words? Do they both use abbreviations, or just one of them, or neither of them? Consider what you know about their characters, and then try to imagine how this would come across over text.
Finally, your assignment is to make sure the famous lines are still recognizable, so before beginning your translation, you may want to highlight these so you make sure they stand out.
Let's review the context of this exchange. Romeo and Juliet have met at Capulet's party. This is the first time they interact, and it seems to be love at first sight. Their families are enemies, but this does not seem to stop them. Romeo sneaks into Juliet's backyard, where he gives a soliloquy about how much he loves her. He overhears Juliet's soliloquy about how she loves Romeo despite the fact that he is a Montague. Romeo calls out to Juliet, which startles her, and she asks how he got there.
In lines 85–127, Romeo says love led him to her balcony. Juliet admits she is blushing in the darkness. If he says he loves her, she'll believe it—but she also recognizes that he might be lying. She admits she has feelings for him too. Romeo swears that he loves her, and she stops him from swearing.
Here's an example of what I imagine their text exchange might look like. Yours will be different, based on what texting style you ascribe to them.
JULIET: How'd you get this number?
ROMEO: Love, bby <3
JULIET: aw, I'm blushing. Do you love me?
JULIET: don't answer, I know you'll say yes, and I believe you, but what if you're lying?
JULIET: I like you too. I think I like you too much. omg i'm triple texting you how embarrassing!
ROMEO: girl i swear by the moon i love u
JULIET: lol don't swear by the moon it's always changing!!!
ROMEO: wat should I swear by?
JULIET: Don't swear at all!
JULIET: on second thought, if you're gonna swear, then swear by yourself because that's what I hold highly, then I'll believe you <3
ROMEO: (...)
JULIET: wait this is all so sudden!
JULIET: i like you, but this is moving too fast, so i'm gonna sign off for the night :3

What an interesting question! I’m having trouble thinking of two forms of English more dissimilar than Shakespearian English and the vernacular used in texting and on social media! The first thing I would recommend is that you exclude or reword the instances where the characters imply that they can see each other. For example,

Thou knowest the mask of night is on my face,Else would a maiden blush bepaint my cheek

Here, you might say,

im blushing, lucky its dark here.

Or, where they talk about their physical location—

Lady, by yonder blessed moon I vow.

You might say,

I swear on the moon I can see out the window.

Unaltered, such references don’t make sense in text conversations, where we should assume that the participants are in different places.
A second technique you might think about using is abbreviation. You could take a word like “love” and transform it to “luv.” Since the language used in texts is a dynamic language which people are adding to all the time, you can be really inventive here. As one more example, each time a character uses the word “too,” as in

It is too rash, too unadvis’d, too sudden,

You might substitute the number 2 in its place.
Shakespeare’s dialogs are typically written in long iambic lines meant to express elaborate ideas, a style of writing that does not lend itself at all well to texting. One solution to this disjunction might be to take ideas that, due to the elaborate language he used to express them, Shakespeare had to put on different lines, and simplify them so that they fit into single sentences:

Dost thou love me? I know thou wilt say, “Ay,”And I will take thy word; yet, if thou swear’st,Thou mayest prove false: at lovers’ perjuries.

Here Juliet does three things. Firstly, she poses Romeo a question when she asks him if he loves her. Then, she states her belief that he will say yes and that she will believe him when he says it. But then she backtracks by saying that, in fact, if he does say he loves her, he might not be speaking honestly. By moving things around, I can make these three things fit neatly into one comparatively short sentence:

Do you love me? I think you’ll say yes, and I’ll believe you if you do, but you might not be telling the truth.

See how Juliet’s words, which would take far too long to express in the form of a text message, can be reduced into a far more manageable form?