Eadem femina liberalis dicit amicitiam magis quam pecuniam valere, sed mercator avarus hoc non intellegit.

Because eadem has to agree with femina in gender, number, and case.

• femina is feminine singular nominative
• so the form of idem, eadem, idem must also be feminine singular nominative
• that form is eadem

So eadem femina means the same woman.

Here liberalis is an adjective describing femina.

It can mean things like:

• generous
• noble-minded
• open-handed

So femina liberalis is a generous woman or a noble-minded woman.

Grammatically, liberalis is nominative singular feminine here, agreeing with femina, even though its form could also look masculine in some contexts. The noun femina makes it clear that it is feminine here.

They are accusative because of the construction after dicit.

Latin often uses an accusative + infinitive construction after verbs of saying, thinking, knowing, and so on. Here:

• dicit = she says
• amicitiam ... valere = literally friendship to be worth / to prevail

So amicitiam is the subject of the infinitive valere, but in an indirect statement that subject goes into the accusative.

pecuniam is also accusative because it is being compared with amicitiam in the phrase magis quam pecuniam.

So the structure is:

• dicit
  • amicitiam ... valere
• she says that friendship is worth more than money

This is the very common Latin indirect statement construction.

Instead of saying:

• She says that friendship is worth more than money

Latin says:

• She says friendship to be worth more than money

That is why you get:

• dicit = says
• amicitiam = accusative subject of the infinitive
• valere = infinitive

So:

• dicit amicitiam magis quam pecuniam valere
• literally: she says friendship to be worth more than money
• natural English: she says that friendship is worth more than money

Valere has several related meanings in Latin, including:

• to be strong
• to be well
• to have power
• to be worth
• to count for more

In this sentence, it means something like:

• to be worth more
• to matter more
• to have greater value

So amicitiam ... valere means that friendship has greater worth or importance.

Magis quam means more than.

Since valere is a verb, the comparison is being made adverbially:

• magis quam pecuniam valere = to be worth more than money

This is a standard way to express comparison.

You can think of it as:

• magis = more
• quam = than

So the sentence says friendship counts for more than money.

Not naturally in this exact structure.

Because the key idea is expressed through the verb valere, Latin uses magis to modify the verbal idea: to be worth more.

If Latin were comparing two nouns with an adjective, a comparative adjective might be more likely. But here the comparison belongs with the verb, so magis quam is the straightforward choice.

Hoc means this, and here it is a neuter singular accusative demonstrative pronoun.

It refers not to one single noun, but to the whole preceding idea:

• that friendship is worth more than money

So:

• hoc non intellegit
• he does not understand this

Using the neuter singular to refer to an entire statement or idea is very common in Latin.

Both word orders are possible in Latin.

Because Latin has case endings, word order is more flexible than in English. So both of these can mean:

• mercator avarus
• avarus mercator

= the greedy merchant

In this sentence, mercator avarus may simply be the chosen word order, or it may leave a little more weight on avarus at the end of that noun phrase.

Because its subject is mercator avarus, which is singular:

• mercator = merchant
• avarus = greedy
• together: the greedy merchant

So the verb must also be singular:

• intellegit = he understands

With non:

• non intellegit = he does not understand

Because Latin has no articles.

So:

• femina can mean a woman or the woman
• mercator can mean a merchant or the merchant

The exact sense depends on context.

That is why eadem femina can be understood as the same woman, even though Latin does not have a separate word for the.

Yes. Sed is the standard Latin conjunction meaning but.

It connects the two contrasting ideas:

• the woman says friendship is worth more than money
• but the greedy merchant does not understand this

So sed marks the contrast very clearly.

It is fairly natural Latin word order.

A rough outline is:

• Eadem femina liberalis — subject
• dicit — main verb
• amicitiam magis quam pecuniam valere — indirect statement
• sed mercator avarus hoc non intellegit — contrasting main clause

Latin often puts the verb later than English would, and it often places important or contrasting words in noticeable positions. But nothing here is especially strange; it is a good example of normal Latin flexibility.