La fleuriste prépare un petit bouquet afin que nous puissions remercier notre voisine.

Fleuriste means florist. In this sentence, la fleuriste means the florist.

A couple of useful points:

• le fleuriste = the florist (male)
• la fleuriste = the florist (female)

French usually uses an article before a noun like this when it is the subject of the sentence. So English The florist prepares... becomes La fleuriste prépare...

In French, many common short adjectives often come before the noun, and petit is one of them.

So:

• un petit bouquet = a small bouquet

Also, petit agrees with bouquet:

• bouquet is masculine singular
• so the adjective is petit (masculine singular)

If the noun were feminine, you would usually get petite instead.

Afin que means so that or in order that.

It introduces a clause of purpose. In other words, it explains why the florist is preparing the bouquet.

So the structure is:

• La fleuriste prépare un petit bouquet
• afin que nous puissions remercier notre voisine

= The florist is preparing a small bouquet so that we can thank our neighbor.

A useful note: afin que is a bit more formal than pour que, but both often mean the same thing in practice.

Because afin que is followed by the subjunctive in French.

So after afin que, you do not say:

• afin que nous pouvons ❌

You say:

• afin que nous puissions ✅

Here, puissions is the present subjunctive form of pouvoir for nous.

This is one of the most important patterns to learn:

• afin que + subjunctive
• pour que + subjunctive

Puissions is the nous form of the present subjunctive of pouvoir (to be able to / can).

Present subjunctive of pouvoir:

• que je puisse
• que tu puisses
• qu’il / elle / on puisse
• que nous puissions
• que vous puissiez
• qu’ils / elles puissent

In the sentence, que nous puissions remercier literally means something like that we may be able to thank, but in natural English you would usually just say so that we can thank.

Because remercier takes a direct object in French.

So:

• remercier quelqu’un = to thank someone

That is why the sentence says:

• remercier notre voisine = to thank our neighbor

This is different from:

• dire merci à quelqu’un = to say thanks to someone

Compare:

• Nous remercions notre voisine.
• Nous disons merci à notre voisine.

Both can translate to We thank our neighbor, but the grammar is different.

Notre means our, and voisine means female neighbor.

So:

• notre voisin = our male neighbor
• notre voisine = our female neighbor

A useful detail: notre does not change for masculine vs. feminine singular nouns.

So you say:

• notre voisin
• notre voisine

It only changes for number:

• notre = our (singular noun)
• nos = our (plural noun)

Because it is the feminine form of voisin.

• voisin = male neighbor / masculine form
• voisine = female neighbor / feminine form

Here the sentence is referring to a female neighbor, so French uses voisine.

This feminine ending is very common in French:

• ami / amie
• étudiant / étudiante
• voisin / voisine

Very natural in French. In English, the most natural translation is usually:

• so that we can thank our neighbor

If you translate word-for-word, it looks more like:

• so that we may be able to thank our neighbor

But English normally does not show the subjunctive here the way French does. So when reading French, it is best to understand:

• afin que + subjunctive
  as
• so that...

without trying to force a very literal English version every time.

Like this:

• La fleuriste = the florist
• prépare = prepares / is preparing
• un petit bouquet = a small bouquet
• afin que = so that / in order that
• nous puissions = we can / we may be able to
• remercier = thank
• notre voisine = our neighbor

So the basic structure is:

subject + verb + object + purpose clause

That is:

• La fleuriste prépare un petit bouquet
  main clause

• afin que nous puissions remercier notre voisine
  purpose clause, introduced by afin que and using the subjunctive