Ars figulina amicae placet.

Because ars is in the nominative singular, which is the normal case for the subject.

• ars = art / skill / craft
• figulina describes ars, so together they mean something like pottery, the potter’s craft, or ceramic art

So the thing doing the grammatical action of pleasing is ars figulina.

Because amicae is in the dative singular, not the nominative.

With placet, the person who experiences the pleasure is usually put in the dative:

• amicae = to the friend or to the female friend

So the structure is not the friend likes pottery in a literal Latin sense. It is more like:

• Pottery is pleasing to the friend

That is why amicae is not the subject.

Because placeo, placere works differently from English like.

In English, we say:

• The friend likes pottery

But in Latin, with placeo, the idea is:

• Pottery pleases the friend
• literally, Pottery is pleasing to the friend

So Latin makes the thing liked the subject, and the person who likes it goes into the dative.

Here amicae means to the friend or to the female friend.

The base word is amica, meaning female friend.
The ending -ae can have several possible meanings in Latin, but in this sentence the verb placet tells us that it should be understood as dative singular:

• amicae = to/for the female friend

So the sentence is talking about what is pleasing to her.

Because figulina matches ars in gender, number, and case.

• ars is feminine singular nominative
• figulina is also feminine singular nominative

That agreement shows that figulina is an adjective modifying ars.

So ars figulina is one unit: pottery art, the potter’s craft, or simply pottery.

Because its subject, ars figulina, is singular.

The main noun is ars, which is singular, so the verb must also be singular:

• ars figulina placet = pottery pleases
• if the subject were plural, Latin would use placent

So placet agrees with ars, not with amicae.

Yes. Latin word order is much freer than English word order because the endings show the grammatical roles.

For example, these could mean the same basic thing:

• Ars figulina amicae placet
• Amicae ars figulina placet
• Ars amicae figulina placet

Writers may change the order for emphasis, rhythm, or style.
Even so, placet still goes with ars figulina, and amicae still means to the friend.

Because Latin has no articles like English the or a/an.

So ars figulina amicae placet could be understood in English as:

• Pottery pleases the friend
• The potter’s craft pleases a friend
• Ceramic art is pleasing to the friend

Which English article sounds best depends on context, not on a separate Latin word.

Here it is an adjective.

It comes from figulinus, figulina, figulinum, meaning something like potter’s, ceramic, or made by a potter. Since it agrees with ars, it describes that noun.

So:

• ars = art / craft
• figulina = pottery-related / ceramic / potter’s

Together they form the idea the craft of pottery or simply pottery.

Yes. The form amicae is ambiguous by itself. Depending on context, it could be:

• genitive singular = of the female friend
• dative singular = to/for the female friend
• nominative plural = female friends

But in this sentence, placet strongly points to the dative singular meaning, because placeo commonly takes the person affected in the dative.

So here amicae means to the female friend, not of the friend or female friends.