Discipuli gaudent, quod et cervum et cervam simul videre possunt.

Discipuli is nominative plural, and it means the students. It is the subject of the main verb gaudent.

Its dictionary form is discipulus, -i (student, masculine). The singular would be discipulus; the plural nominative is discipuli.

So:

• discipulus = one student
• discipuli = students

Because the subject is discipuli, which is third person plural (they), the verb must also be third person plural.

From gaudeo, gaudere (to rejoice, be glad):

• gaudeo = I am glad
• gaudes = you are glad
• gaudet = he/she/it is glad
• gaudemus = we are glad
• gaudetis = you all are glad
• gaudent = they are glad

Since discipuli = the students / they, Latin uses gaudent.

Here quod means because.

It introduces a clause giving the reason why the students are glad:

• Discipuli gaudent = The students are glad
• quod ... possunt = because they are able ...

So this is a causal clause.

A learner may already know quod as which or the fact that, but in this sentence it is best understood as because.

Because this is a straightforward statement of real cause: the students are glad because they really can see both animals.

Latin often uses quod + indicative when the cause is presented as an actual fact.

So:

• quod ... possunt = because they can

This is normal and expected here.

Et ... et ... means both ... and ....

So:

• et cervum et cervam = both the male deer and the female deer

If Latin used only one et, the sense would just be and. But et ... et ... gives emphasis to the fact that both are seen.

Compare:

• cervum et cervam = a male deer and a female deer
• et cervum et cervam = both a male deer and a female deer

They are both in the accusative singular because they are the direct objects of videre (to see).

• cervus = male deer / stag
• cervum = a male deer / stag as direct object
• cerva = female deer / hind
• cervam = a female deer / hind as direct object

Since the students are seeing these animals, Latin puts them in the accusative:

• videre cervum = to see a male deer
• videre cervam = to see a female deer

They are masculine and feminine forms meaning different animals by sex:

• cervus = a male deer, often a stag
• cerva = a female deer, often a hind

So the sentence is specifically saying that the students can see one male deer and one female deer.

This is why the sentence uses both words, not just one general word for deer.

Because possum means to be able / can, and after possum Latin normally uses an infinitive.

So:

• videre = to see
• possunt = they are able / they can

Together:

• videre possunt = they can see

This is exactly like English can see.

Compare:

• vident = they see
• videre possunt = they can see / are able to see

It is an infinitive because it depends on possunt.

In Latin, modal verbs such as possum are commonly followed by an infinitive:

• possum currere = I can run
• potest dormire = he/she can sleep
• possunt videre = they can see

So videre is not the main finite verb of the clause. The finite verb is possunt.

Simul means at the same time, together, or simultaneously.

Here it modifies the idea of seeing:

• et cervum et cervam simul videre possunt
  = they can see both the male deer and the female deer at the same time

It adds the detail that the two animals are visible together, not separately.

Latin word order is much freer than English word order. A verb often comes at or near the end of its clause, especially in straightforward prose.

So:

• videre possunt
• literally: to see they are able
• natural English: they can see

Putting possunt at the end is completely normal Latin. It also lets the sentence build toward the main idea of the reason clause.

Yes. Latin does not need to repeat the subject if it is already clear from the verb ending.

In possunt, the ending -nt tells you the subject is they.

So the sentence means:

• The students are glad, because they can see both the male deer and the female deer at the same time.

Latin does not need to say discipuli ... quod discipuli ... possunt unless it wants extra emphasis.

Yes. That would still be understandable Latin.

Because Latin word order is flexible, several arrangements are possible. However, et cervum et cervam simul videre possunt is a neat and natural order:

1. the two objects are presented,
2. then simul adds together / at the same time,
3. and finally possunt completes the thought.

So the given order is stylistically natural, even though other orders are possible.