OK, let’s say that $1 US is worth 6 francs (French).
And that $1 US is worth 4 marks (German).
And that 1 pound (British) is worth $1.50.
Does that mean that 1 pound is worth 9 francs?
Or that 1 pound is worth 6 marks?
Is 1 mark worth 1.5 francs?
In other words, are currency exchange rates consistent with each other?
Yes. Because if they are not you can make riskless profit by simultaneous selling and buying in appropriate currencies (triangular arbitrage). Arbitrage activity would very rapidly eliminate any inconsistency, on currency markets probably in less than a second.
Oh and in the example you gave the mark and the franc are now fixed together in the euro.
Keep the following in mind–
If you are traveling abroad, most moneychangers charge a fee for exchanging money. In your example 1 US dollar equals 6 francs, but you might get only 5.7. Then when returning you might get only 95 cents for 6 francs. If you are planning on spending a lot of money, it pays to think ahead about exchanging it and comparing rates.