Por ejemplo, el hombre trabaja en casa.

Por ejemplo means for example. It is used to introduce an example that supports or illustrates something said before.

In this sentence, it is not part of the core grammar of el hombre trabaja en casa. It is just an introductory phrase. If you remove it, the sentence still works:

El hombre trabaja en casa. = The man works at home.

The comma after por ejemplo is standard because it is an introductory expression.

Because el hombre means the man.

In Spanish, singular countable nouns usually need an article or some other determiner in normal sentences. So hombre trabaja en casa would sound incomplete in standard Spanish.

• el hombre = the man
• un hombre = a man

So if you want to say the man works at home, el hombre is the natural form.

Trabaja is the third-person singular present tense form of the verb trabajar.

The subject is el hombre, which is grammatically he / the man, so the verb must match that subject.

Present tense of trabajar:

• yo trabajo = I work
• tú trabajas = you work
• él / ella / usted trabaja = he / she / you work
• nosotros trabajamos = we work
• vosotros trabajáis = you all work
• ellos / ellas / ustedes trabajan = they / you all work

So el hombre trabaja = the man works.

It can mean either, depending on context.

The Spanish present tense often covers both:

• a habitual action: The man works at home
• a current action: The man is working at home

If you want to make right now especially clear, Spanish often uses estar + gerund:

El hombre está trabajando en casa. = The man is working at home.

But in many situations, simple present trabaja is enough.

En casa is the usual idiomatic way to say at home.

Spanish often leaves out the article in this expression:

• Estoy en casa. = I am at home.
• Trabaja en casa. = He works at home.

En la casa is also possible, but it usually sounds more like in the house or at the house, referring to a specific building rather than the general idea of home.

So:

• en casa = at home
• en la casa = in/at the house

Yes, and it is very common.

There is a slight difference:

• trabaja en casa = he works at home
• trabaja desde casa = he works from home

In many real-life situations, especially talking about remote work, desde casa is often more natural. But en casa is still correct and understandable.

Because Spanish does not usually need subject pronouns when the subject is already clear.

Here the subject is explicitly stated as el hombre, so adding él would be unnecessary.

Spanish commonly says:

• El hombre trabaja en casa.

Not usually:

• Él el hombre trabaja en casa. ❌

You can use él only for emphasis or contrast, but not together with el hombre in that way.

The normal word order here is:

Por ejemplo, el hombre trabaja en casa.

That is the most neutral and natural order:

• introductory phrase
• subject
• verb
• place expression

Spanish word order is somewhat flexible, but changes usually add emphasis or sound more literary. For example:

• El hombre trabaja en casa. = neutral
• En casa trabaja el hombre. = unusual, more emphatic or contrastive

For learners, the original order is the safest choice.

In Spanish, h is silent. So hombre is pronounced roughly like OM-breh.

A few helpful points:

• h is not pronounced
• the o is a short, clear vowel
• mb is pronounced together naturally
• the r in hombre is a light Spanish r, not a strong English-style r

So the beginning is not hom- in the English sense; it starts essentially with the vowel sound.

In this expression, it is best to learn por ejemplo as a fixed phrase meaning for example.

Trying to translate por word by word here is not very helpful. On its own, por can mean several things, such as by, through, because of, or for, depending on context. But in por ejemplo, the whole phrase simply functions as for example.

So for learners, the easiest approach is:

• memorize por ejemplo as one chunk
• use it to introduce examples

Example: Por ejemplo, mi hermana estudia por la noche. = For example, my sister studies at night.