Embargo
 

How can I translate into English embargo in the following contexts:

Me han embargado el piso. = it means that I did´t pay my debts and at some point they can take it.
Tiene dos embargos en su casa.= I failed to pay my taxes or m y mortgage or some debts and if I want to sell it I have to pay the debts.

Without more context, I perceive your examples as referring to a legal process. Your first sentence uses the verb "embargar", and the other sentence uses the noun "embargo".

Some possible translations for the verb include: foreclose, repossess, seize, freeze, garnish, and possibly hold a lien.

Some possible translations for the noun include: foreclosure, repossession, seizure, freezing, garnishment, and lien.

These words are all the names of different types of legal recourse that a lender has when a borrower fails to pay a debt or to repay a loan according to the terms of the loan contract.

I AGREE But how can I put them in the sentences above?
The bank has seizure my apartment?
I have two liens on my business?

The bank has seized/repossessed/foreclosed my ...

I have two liens ...
I am in foreclosure ...

My wages are (being) garnished (in order to repay a lien/debt).

There's a problem of different legal systems here.

The Spanish word embargo might involve the right to keep possession of the embargado's property, but generally it only implies the property can't be sold and it's kept under the owner's control but reserved to be eventually auctioned if the owner fails to pay their debts only in the case a judge, after legal procedures, determines so.

I'm not using the word "owner" lightly. Laws of Latin origin consider real estates to be part of civil law, not trade law, so you own your real estate even if it's mortgaged. The mortgage itself is a right in rem independent of ownership, so banks can't foreclose your real estate -the cannot "repossess" what was never ever theirs-. If the mortgage is not paid the creditor has the right to start a juicio de ejecución hipotecaria which will eventually end up with the property being sold to pay the mortgage and costs and with any remaining sum being given to the owner (who is never the bank).

I have two lines in my apartment?
I am in foreclosure with my apartment?

In the US, apartments are rented, usually with month-to-month payments (an upfront deposit, usually the same as one-month's rent, is often required). Most sign a contract that specifies how long we will make monthly payments. If we've been a good tenant for the duration of the contract, we are entitled to a refund (or partial refund, if our contract so states) of the deposit.
I've never heard of anyone buying an apartment.
Stepping it up a bit, buying a condominium is common if a person doesn't want to take on the additional responsibilities of home ownership.
In order to buy a condo, a unit in a complex, or a house, we often take out a mortgage (unless we can afford to buy the property outright).

Once we have a mortgage, there is a lien associated with it (a lien is a legal right or interest that the lender has in your property until the mortgage is paid off).

The lien gives the lender the right to foreclose your property if you fail to make the payments as stated in the closing (lending) documents.

When we take out a second mortgage on real estate (usually done only when emergency cash is needed), we would then have a second lien. Both mortgages must be paid off before those liens are lifted.