Hoc periculum maius est quam illud.

Because periculum is a neuter singular noun, and the demonstrative must agree with it.

• hic = masculine singular
• haec = feminine singular
• hoc = neuter singular

Since the noun is periculum, Latin uses hoc periculum for this danger.

It is nominative singular.

You can tell because:

• periculum is the subject of est
• hoc agrees with periculum in gender, number, and case

So hoc periculum is the thing being described as greater.

Because maius is the neuter nominative singular form of the comparative adjective.

The comparative of magnus (big, great) is:

• maior for masculine/feminine
• maius for neuter

Since periculum is neuter, the adjective must also be neuter:

• hoc periculum maius est

Yes. Maius is a comparative adjective meaning greater or bigger.

It agrees with periculum in:

• gender: neuter
• number: singular
• case: nominative

So it describes periculum directly: this danger is greater.

Because magnus has an irregular comparative and superlative pattern:

• positive: magnus = great, large
• comparative: maior / maius = greater
• superlative: maximus = greatest

So maius is exactly the form you should expect from magnus, even though it does not look very close to the positive form.

Quam means than in a comparison.

So the structure is:

• maius ... quam ...
• greater ... than ...

It links the two things being compared:

• hoc periculum = this danger
• illud = that one / that danger

Because Latin often leaves out a noun when it is obvious from the context.

So illud here really means:

• illud periculum = that danger

English does the same thing sometimes:

• This danger is greater than that one

Latin simply uses the demonstrative by itself, with the noun understood.

It is best understood as nominative singular neuter, with periculum left out.

So the full underlying comparison is:

• Hoc periculum maius est quam illud periculum

Because the omitted noun would be nominative, illud is nominative too.

Yes, often Latin can express comparison in two ways:

• maius quam illud
• illo maius

Both can mean greater than that.

In this sentence, the author uses quam + the same case instead of the ablative of comparison. That is a very common and clear way to make a comparison.

Because the subject is singular:

• hoc periculum = this danger

So the verb must also be singular:

• est = is

If the subject were plural, Latin would use sunt instead.

Yes, the word order can vary.

Latin word order is more flexible than English because the endings show the grammar. This sentence could be rearranged in several ways without changing the basic meaning, for example:

• Hoc periculum maius est quam illud
• Maius est hoc periculum quam illud
• Hoc maius periculum est quam illud (with a slightly different feel)

The original order is straightforward and natural, but Latin often moves words for emphasis.

Because Latin does not have definite or indefinite articles like English the or a/an.

So:

• hoc periculum can mean this danger
• illud can mean that one or that danger

Whether English uses the, a, or nothing depends on context and translation style, not on a separate Latin word.

They are both forms of the demonstrative pronoun/adjective hic, haec, hoc and ille, illa, illud.

In this sentence:

• hoc is used adjectivally, because it directly modifies periculum
• illud is used pronominally, because it stands by itself and replaces illud periculum

So Latin uses demonstratives both:

• as adjectives: this danger
• as pronouns: that one

Because ille, illa, illud is the standard demonstrative for that.

Its basic forms are:

• ille = masculine
• illa = feminine
• illud = neuter

Since the understood noun is periculum, which is neuter singular, Latin uses illud.

Yes. Periculum is a neuter second-declension noun.

That affects several words in the sentence:

• hoc is neuter because it modifies periculum
• maius is neuter because it agrees with periculum
• illud is neuter because it stands for the omitted periculum

So the neuter gender of periculum shapes much of the grammar of the whole sentence.