Culter huic operi aptus est.

Because culter is in the nominative singular, and it also matches aptus est in number and gender.

• culter = knife
• aptus = suited / suitable / fitted
• est = is

So culter ... aptus est means the knife is suitable. In other words, culter is the thing being described.

Because aptus must agree with culter.

In Latin, adjectives agree with the nouns they describe in:

• gender
• number
• case

Culter is masculine singular nominative, so the adjective must also be masculine singular nominative: aptus.

If the noun were feminine, you would expect apta. If it were neuter, you would expect aptum.

Because they are not the subject. They form a phrase meaning for this work / for this task.

Here aptus takes the dative to show the thing for which something is suited. So:

• operi = for the work / task
• huic operi = for this work / task

A native English speaker often expects a preposition such as for, but Latin can express that idea just by using the dative case.

Because huic is the dative singular form of hic, haec, hoc.

Since operi is dative singular, the demonstrative modifying it must also be dative singular:

• nominative/accusative neuter singular: hoc
• dative singular: huic

So huic operi means for this task/work, not simply this task/work.

Because the dictionary form opus is the nominative singular, but here the word is in the dative singular after aptus.

The noun is:

• opus = nominative singular
• operis = genitive singular

From that stem, the dative singular is operi.

So:

• opus = work, task
• operi = for the work / task

It is one phrase.

Huic is a demonstrative adjective modifying operi. They agree with each other in:

• case: dative
• number: singular
• gender: neuter

So you should understand them together as for this task or for this work.

Because Latin often uses case endings where English uses prepositions.

English says:

• suitable for this task

Latin says:

• aptus huic operi

The idea of for is built into the dative case. This is very common in Latin, especially with certain adjectives.

Latin word order is much freer than English word order because the endings show what each word is doing.

So Culter huic operi aptus est is perfectly normal. Putting est at the end is very common in Latin prose.

English depends heavily on word order, but Latin depends much more on inflection. That means the sentence could often be rearranged without changing the basic meaning.

Yes. For example, Latin could also say:

• Culter aptus huic operi est
• Huic operi culter aptus est
• Aptus est culter huic operi

These all mean essentially the same thing, though the emphasis may shift slightly.

The given order is a natural one, but not the only possible one.

Latin has no articles. There is no separate word for a, an, or the.

So culter can mean:

• a knife
• the knife

and opus can mean:

• a task
• the task
• work

The translator chooses the most natural English wording from the context.

Aptus means something like:

• suited
• suitable
• fit
• appropriate
• well adapted

So the sentence is saying that the knife is the right tool for this particular work/task.

It does not necessarily mean the knife is morally good or beautiful; it means it is well suited to the purpose.