Puedo contar con mi familia cuando tengo un problema.

By itself, contar often does mean to count or to tell:

• contar números = to count numbers
• contar una historia = to tell a story

But contar con is a fixed expression that means to count on, to rely on, or to depend on someone or something.

So in this sentence:

Puedo contar con mi familia = I can count on my family

You should learn contar con as a unit.

Because contar con is the standard expression in Spanish for to rely on / count on.

• contar con alguien = to count on someone
• contar con algo = to have, rely on, or be able to use something

Using en here would be incorrect. This is just a case where the preposition is part of the expression and must be memorised.

Puedo is the yo form of poder, which usually means can or to be able to.

So:

• puedo contar = I can count
• puedo contar con mi familia = I can count on my family

Here it expresses ability or possibility in the sense of being able to rely on them.

Spanish often leaves out subject pronouns when they are not needed, because the verb ending already shows who the subject is.

• puedo already tells you it means I can
• tengo already tells you it means I have

So:

• Puedo contar con mi familia... = I can count on my family...
• Yo puedo contar con mi familia... is also possible, but it adds emphasis

You might include yo if you want contrast or emphasis, such as Yo puedo contar con mi familia, pero él no.

In modern Spanish, you normally do not use an article before a possessive adjective like mi, tu, su, etc.

So you say:

• mi familia = my family
• mi casa = my house
• mis amigos = my friends

Not la mi familia.

Because familia in Spanish, like family in English, is usually treated as a singular collective noun.

So:

• mi familia = my family

Even though a family contains several people, the noun itself is singular.

If you wanted to refer to family members individually, you could say something like mis familiares or los miembros de mi familia, but mi familia is the normal and natural choice here.

Because this sentence is talking about something general or habitual: when(ever) I have a problem.

With cuando, Spanish often uses the indicative when referring to repeated, usual, or real situations:

• cuando tengo un problema = when I have a problem / whenever I have a problem

You are not talking about a future uncertain event in a way that triggers the subjunctive here. This is a general truth or regular situation.

It can feel like either in English, depending on context.

In this sentence:

cuando tengo un problema

it often has the sense of when(ever) I have a problem — meaning any time that situation happens.

So the sentence suggests a repeated or dependable pattern: whenever a problem comes up, I can rely on my family.

Un problema means a problem in a general singular sense.

So the sentence means:

• when I have a problem

If you said cuando tengo problemas, that would mean when I have problems, which is also possible, but slightly changes the nuance:

• un problema = a problem, any one problem that comes up
• problemas = problems in general or multiple problems

Both can be natural, but the singular is very common in this kind of sentence.

Yes. Problema is masculine:

• un problema
• el problema

This is one of those Spanish nouns that end in -a but are still masculine, often because they come from Greek-origin words.

Other similar examples are:

• el sistema
• el programa
• el tema

So you should memorise problema as a masculine noun.

Yes. That is a very good translation.

Contar con can often be translated as:

• count on
• rely on
• depend on

So all of these are close in meaning:

• I can count on my family when I have a problem
• I can rely on my family when I have a problem

The exact English wording may change, but the Spanish structure stays the same.

Yes, and it is very natural.

The difference is subtle:

• Puedo contar con mi familia... = I can count on my family...
• Cuento con mi familia... = I count on my family / I rely on my family

Using puedo highlights the idea that your family is available and dependable to you.
Using cuento con sounds a bit more direct and confident: you do rely on them.

Both are correct, but puedo contar con is especially common when expressing reassurance or support.

The given order is the most neutral and natural:

Puedo contar con mi familia cuando tengo un problema.

But Spanish word order can change for emphasis. For example:

• Cuando tengo un problema, puedo contar con mi familia.

This means the same thing, but it puts the time/situation first: When I have a problem, I can count on my family.

So the order is flexible, but the original version is perfectly standard.

It is standard Spanish and would be understood everywhere in the Spanish-speaking world.

Nothing in this sentence is uniquely Spain-specific. A speaker in Spain, Mexico, Argentina, or elsewhere could all say it naturally.

So it is a very useful sentence to learn in general Spanish, not just Spanish from Spain.