Η φίλη μου γυμνάζεται στο σπίτι όταν δεν προλαβαίνει να πάει στο γυμναστήριο.

Yes. Η φίλη μου means my friend, specifically my female friend.

• η = the for a feminine singular noun
• φίλη = female friend
• μου = my

Greek usually keeps the definite article with possessives, so η φίλη μου is the normal way to say my friend.

If you wanted male friend, you would say ο φίλος μου.

In Greek, unstressed possessive words like μου, σου, του, της usually come after the noun.

So:

• η φίλη μου = my friend
• το σπίτι μου = my house
• ο αδερφός της = her brother

This is one of the most common differences from English word order.

Γυμνάζεται means he/she exercises, works out, or trains.

It comes from the verb γυμνάζομαι, which is very commonly used for physical exercise. In this sentence it means:

• Η φίλη μου γυμνάζεται = My friend works out

Even though the form looks like a passive/middle ending, you should learn γυμνάζομαι as a normal verb meaning I exercise.

Στο is the contraction of σε + το.

• σε = in, at, to
• το = the for a neuter noun
• σε το becomes στο

So:

• στο σπίτι = at home / in the house
• στο γυμναστήριο = to the gym / at the gym, depending on the verb

This contraction is extremely common in everyday Greek.

Because the verb tells you whether the phrase is about location or movement.

• γυμνάζεται στο σπίτι: the action happens there, so it means at home
• να πάει στο γυμναστήριο: πάει means go, so it means to the gym

Greek σε + article can cover in, at, or to, and the verb usually makes the meaning clear.

Όταν means when.

In this sentence, it introduces a repeated or habitual situation:

• Η φίλη μου γυμνάζεται στο σπίτι όταν δεν προλαβαίνει...
• My friend works out at home when she doesn’t have time...

So it is not talking about one single special occasion only. It describes what she generally does in that situation.

Προλαβαίνει is a very useful Greek verb. It often means:

• to have enough time
• to manage to
• to make it in time

So δεν προλαβαίνει να πάει στο γυμναστήριο means something like:

• she doesn’t have time to go to the gym
• she can’t make it to the gym in time

It is a little richer than just has time, because it often suggests that time is short and the person cannot fit the action in.

Because after verbs like προλαβαίνω, Greek normally uses a να-clause.

So:

• προλαβαίνει να πάει = she manages / has time to go

The word να introduces the subordinate verb, roughly like English to in this kind of sentence.

A very important point: Greek does not use an infinitive the way English does here. Instead of to go, Greek uses να + a verb form.

This is about aspect, which is very important in Greek.

• να πάει = aorist subjunctive
• να πηγαίνει = present subjunctive

Here να πάει is more natural because it refers to one trip to the gym, seen as a single whole action: go to the gym.

Να πηγαίνει would sound more like the process or repeated/ongoing action of going, which is not the main idea here.

So Greek prefers:

• δεν προλαβαίνει να πάει στο γυμναστήριο

because the focus is simply on whether she can make that trip or not.

Because δεν negates the finite verb προλαβαίνει.

So:

• δεν προλαβαίνει να πάει = she doesn’t have time/manage to go

In other words, what is negated is the managing / having time, not directly the going.

This is different from negating the να-clause itself. If you wanted to negate the να verb, Greek would use μη(ν), for example:

• πρέπει να μην πάει = she must not go

So remember:

• δεν negates ordinary finite verbs
• μη(ν) is used with να forms and certain other constructions

The sentence uses the present tense for all the main ideas:

• γυμνάζεται
• προλαβαίνει

This gives a habitual meaning, describing what she generally does:

• She works out at home when she doesn’t have time to go to the gym.

So the sentence is not mainly about one specific day. It describes a regular pattern.

Yes, in modern everyday Greek το γυμναστήριο very commonly means the gym or fitness center.

So here:

• να πάει στο γυμναστήριο = to go to the gym

Depending on context, it can sometimes refer to a school gym or sports hall, but in a sentence about exercising, gym is the natural meaning.