Bona fortuna viatorem per viam tutam ducit.

Because the verb ducit needs a subject, and bona fortuna is the phrase that fits that role.

More specifically:

• viatorem is clearly accusative singular, so it is the direct object.
• per viam tutam is a prepositional phrase, so it is not the subject.
• That leaves bona fortuna as the thing doing the action.

A useful extra point: if you do not write macrons, bona fortuna could look like either nominative or ablative. With macrons, the difference is clearer:

• nominative: bona fortūna
• ablative: bonā fortūnā

In this sentence, the syntax shows that it is nominative, so it is the subject.

Because fortuna is a feminine noun, and Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

Since fortuna is feminine singular, the adjective must also be feminine singular: bona.

So:

• bonus = masculine
• bona = feminine
• bonum = neuter

Because it is the direct object of ducit.

The basic noun is viator = traveler.
But when a third-declension masculine noun is used as a direct object in the singular, it usually takes the accusative ending -em:

• nominative: viator
• accusative: viatorem

So viatorem means that the traveler is the one being led.

Ducit is:

• 3rd person
• singular
• present tense
• active voice
• indicative mood

It comes from the verb ducere, meaning to lead.

So ducit means he/she/it leads or is leading, depending on context.
Here the subject is bona fortuna, so the sense is good fortune leads.

Because per takes the accusative case.

The noun via is first declension:

• nominative singular: via
• accusative singular: viam

Since it follows per, it must be accusative: per viam.

This is a very common Latin pattern:

• per
  • accusative = through, along, by way of

Tutam agrees with viam.

The adjective comes from tutus, tuta, tutum, meaning safe.
Because viam is feminine, singular, and accusative, the adjective must match it:

• viam = feminine singular accusative
• tutam = feminine singular accusative

So tutam describes viam, not viatorem.

That is important because viatorem is masculine accusative singular, so an adjective describing it would need a masculine form, such as tutum, not tutam.

Yes. Latin word order is more flexible than English word order because the endings show the grammatical relationships.

For example, these would still mean essentially the same thing:

• Bona fortuna viatorem per tutam viam ducit.
• Viatorem bona fortuna per viam tutam ducit.
• Per viam tutam bona fortuna viatorem ducit.

The exact word order can change the emphasis, but the case endings still show what belongs together.

Yes, but not in the same way as in English.

In English, word order usually tells you who is doing the action and who receives it.
In Latin, case endings usually do that job instead.

So in this sentence:

• bona fortuna is the subject because of its form and syntax
• viatorem is the object because it is accusative
• per viam tutam is a prepositional phrase because of per

That means the order can change without destroying the meaning.
However, word order still matters for style, emphasis, and rhythm.

Because Classical Latin does not have articles like English the and a/an.

So:

• viatorem can mean the traveler or a traveler
• viam can mean the road or a road

The context tells you which is more natural in translation.

This is very normal in Latin, and learners often have to get used to supplying articles in English even when none are written in the Latin.

Grammatically, it is a normal noun phrase: good fortune.

But stylistically, Latin often lets abstract ideas act like agents:

• fortuna can do things
• virtus can do things
• fama can do things

So bona fortuna viatorem ducit treats good fortune as the force guiding the traveler. That does not have to mean an actual goddess is intended, though Latin literature can sometimes personify Fortuna very strongly.

So the phrase is grammatically ordinary, but it can carry a slightly poetic or personified feeling.

This sentence gives a good mix of common patterns:

• fortuna — first declension noun
• via — first declension noun
• viator — third declension noun
• bonus, bona, bonum — first/second declension adjective
• tutus, tuta, tutum — first/second declension adjective
• ducere — third conjugation verb

That is why you see different endings:

• fortuna / viam
• viatorem
• bona / tutam
• ducit

A lot of Latin reading depends on recognizing those patterns quickly.