Fascinating, Su.Ki. Let me take a shot.

The $10 profit he made on the first transaction is made. It's a fait accompli, it's "money in the bank." It would only be erased if he incurred a $10 loss on the second transaction. But he didn't. 

Suppose you buy a brown goat from Fiona for $60, and sell it to Ray for $61. Then you buy a white sheep for $80 from Lewis, and sell it to Anne for $81. In this case, it should be clear that you made a $1 profit on the goat and another $1 profit on the sheep, for a total of $2.

There are two things that are confusing about the original story. One is that it is the same goat. This is actually irrelevant to the situation, but it feels as if it should be relevant. The second is the equal spacing of the transaction prices.

To score a profit or loss, you have to pair a purchase and a sale. 

The natural way to pair the transactions is $60-then-$70, and $80-then-$90. This is clear when we make it a goat and a sheep, but it is true even if it is all the same goat.

The puzzle tempts you to pair the $70-then-$80 and interpret it as a $10 loss. We're only tempted to do this because it happens to be the same goat. That's where the problem comes.

Dangerous curve ahead! If it's all the same goat, then, just as accounting arithmetic, you could pair the second and third transactions as a $10 loss, but you would also have to account for the first and fourth transactions--buy at $60, sell at $90--so you would have a $30 profit and a $10 loss, for an overall $20 profit.

$0?

 To buy the goat back the second time at $80, he had to use his original $60, plus the $10 profit from the previous transaction, plus an extra $10 which he had to find from somewhere (by begging, borrowing or dipping deeper into his pocket).

The supposed $10 profit he makes on the final sale is therefore cancelled out by this extra $10 he had to invest.  So, he made zero profit.

I'm useless with maths and money, but that's the way I see it.

And yes, your question should be Can you get it? ( we use the bare infinitive - get, go, have etc - following modal verbs such as 'can'). Or, better still, something like "Can you guess the right answer?".

$20

Correction:

Can you get it?

Or even better

Can you get the answer?

I think we all know where the goat trader learned math:

Modern Educayshun: A short film

https://www.italki.com/discussion/183660

Will someone do me a favour and explain where my reasoning went wrong?

If you're a learner of English, please see this as a form of language practice.

Otherwise, please consider it an act of charity towards the numerically challenged. :)