Lucia Marco diligentior est, et plane intellego cur hoc responsum rectum esse dicat.

Because Marco is ablative singular, and after a comparative adjective Latin can express than Marcus with the ablative of comparison.

So:

• Lucia Marco diligentior est = Lucia is more diligent than Marcus

The full alternative would be:

• Lucia diligentior quam Marcus est

Both are correct. Latin often omits quam and uses the ablative instead.

Diligentior is the comparative of diligens, meaning more diligent.

A few useful points:

• positive: diligens = diligent
• comparative: diligentior = more diligent
• superlative: diligentissimus, -a, -um = most diligent

Here diligentior is nominative singular feminine, agreeing with Lucia.

One important detail: in the comparative, masculine and feminine nominative singular use the same form:

• masculine/feminine: diligentior
• neuter: diligentius

Yes. Latin has two common ways to make a comparison:

1. comparative + quam

   • Lucia diligentior quam Marcus est

2. comparative + ablative

   • Lucia Marco diligentior est

The sentence uses the second pattern.

Plane is an adverb, and here it modifies intellego.

So plane intellego means something like:

• I understand clearly
• I fully understand
• I plainly understand

It is strengthening the verb intellego, not describing responsum or rectum.

Because cur hoc responsum rectum esse dicat is an indirect question after intellego.

Latin rule:

• a direct question might use the indicative
• an indirect question normally uses the subjunctive

So:

• direct: Cur hoc responsum rectum esse dicit? = Why does he say this answer is correct?
• indirect: Intellego cur hoc responsum rectum esse dicat. = I understand why he says this answer is correct.

That is why dicat is subjunctive.

Because the main verb is intellego, which is present, so Latin normally uses primary sequence.

In primary sequence:

• action at the same time as the main verb often takes the present subjunctive

So:

• intellego ... dicat = I understand why he says / is saying

If the main verb were past, you would often expect diceret instead:

• intellexi cur ... diceret = I understood why he was saying / said

Because after verbs of saying, thinking, knowing, and similar verbs, Latin often uses an indirect statement, also called accusative + infinitive.

Here:

• dicat = he/she says
• hoc responsum = this answer
• rectum esse = to be correct

So the structure is:

• dicat [hoc responsum rectum esse]
• he/she says that this answer is correct

This is very common Latin syntax.

In this kind of indirect statement, esse is normally expressed when needed with a predicate adjective like rectum.

So:

• hoc responsum rectum esse = this answer to be correct

The adjective rectum needs the infinitive esse to complete the idea. Latin does sometimes omit forms of esse in certain contexts, especially in compact style or poetry, but in normal prose here esse is exactly what you would expect.

Because responsum is neuter singular, and hoc is the neuter singular form of hic, haec, hoc.

Here:

• responsum = neuter singular
• so the demonstrative must also be neuter singular: hoc

Also, in this sentence hoc responsum is the accusative subject of the indirect statement after dicat.

For comparison:

• masculine accusative singular: hunc
• feminine accusative singular: hanc
• neuter accusative singular: hoc

Because rectum agrees with responsum.

Since responsum is:

• neuter
• singular
• accusative

the predicate adjective must also be:

• neuter
• singular
• accusative

So:

• hoc responsum rectum esse

Even though in English we say correct, in Latin the adjective must match the noun grammatically.

The subject is understood, not stated explicitly.

Latin often leaves subject pronouns unstated when the verb ending already shows the person and number. Dicat is third person singular, so it means:

• he says
• she says
• it says

Which one is meant depends on the context. If the surrounding passage has already introduced a person, that person is probably the subject.

Because Latin word order is much more flexible than English word order. The endings show the grammar, so Latin does not rely as heavily on position.

A very literal unpacking would be something like:

• Lucia Marco diligentior est

  • Lucia than-Marcus more-diligent is

• et plane intellego cur hoc responsum rectum esse dicat

  • and clearly I-understand why this answer correct to-be he/she-says

Latin word order often reflects emphasis and style rather than strict grammatical necessity. In this sentence:

• Lucia comes first as the topic
• Marco diligentior keeps the comparison together
• plane is placed near intellego
• esse dicat comes at the end, which is very natural in Latin

Yes, here responsum is a noun meaning answer.

It originally comes from the supine/participle family of respondeo, but in normal usage responsum is a standard neuter noun meaning:

• answer
• reply
• response

So in this sentence, you should simply read:

• hoc responsum = this answer

not as a participle meaning something like the thing having been answered.