AUD to EURO question: ?

No, it means that that the exchange rate is 1.62 AUD to 1 euro. In other words you will get about 6 euros for 10 AUD. The prices in the shops anywhere in Europe reflect local conditions, and local tax regimes, etc.

Wherever you go in the world that does not use the AUD you will have to cope with an exchange rate. 

If you went to the UK you would get about £5.50 GBP for your 10 AUD.

Your limit is your limit, in AUD. So you will have 3,700 euros to spend in Europe.

No, it means the AUD doesn't buy a whole not of EUROS.

Do you mean AUD6000 is your budget or do you somehow think you are only allowed (by the government) to take that amount of money out of the country? 

Look at the A$6,000 as being used to buy something.  If you purchased $6,000 worth of gold the value would still be $6,000.  In this case you are buying $6,000 worth of euros.  You have not lost anything.  You just have a different asset worth $6,000.

Now, if your travel will cost 6,000 EUR you will indeed need to save more (approx $3,730 more).

Before leaving for Greece, spend a little time familiarizing yourself with approximate exchanges.  For example when you buy something in Greece for 10EUR, realize you are spending about A$16. (and every 10 eur is and additional $16)  It will help you keep track of what you are actually spending because for many like myself, foreign currency has a monopoly money feel and somehow gets spent like..... monopoly money unless you pay attention.

Also check with your bank about any additional charges as related to foreign currency transactions.

Also again, should you exchange AUD for EUR, make sure you are aware of exchange rates and charges.  Compare these as well.  Often money exchanges at the airport do not give you the best deal.  In some countries the best exchange is offered at the post office.  I do not know about Greece.

Finally, it can be a temptation to exchange money on the street.  This is a great way to get taken advantage of or worse, robbed.  Not the best idea.

Have a great trip!!

 1.64 Australian Dollars is equivalent to 1 euro.

As you say, $6000 at the exchange rate would give you 3700 Euros.

If you could change the money straight back again (unlikely as there are transaction fees), you would get your $6000 back.

....no.

Euros and Australian Dollars are different currencies.

1 Euro does not equal 1 Australian dollar.

Question makes no sense.

WHERE did you get the rule you may only have $6000?

When you exchange currencies WHY do you think you have lost a huge amount of value? There is a service charge but is only a few percent of the total exchange.

You may have as much money as you wish to carry. Just inform officials when asked HOW MUCH you have. If it is more than their limit you are expected to explain the source of funds.

Declaring is no penalty trying to hide huge sums of cash and it is discovered is something else.