Bank A has a long position in a derivative that pays either $V_1(H)=3$ or $V_1(T)=0$ at at time 1.
The price of the derivative is $V_0=1.2$.
In order to hedge the long position, Bank A proceeds as follows:
First, Bank A borrows 1.2 from Bank B.
Then Bank A invests this amount 1.2 in the money market, by handing it over to Bank C.
Next Bank A sells $-\Delta_0=0.5$ shares of the underlying stock short.
This gives Bank A the amount $-\Delta_0 S_0=2.00$ on hand, which it invests in the money market, giving $(1+r)2.00=2.50$ at time 1.
The debt to Bank B becomes $(1+r)1.2=1.50$ at time 1. Thus the proceeds from the short sale, and the debt to Bank B,
together add up to $2.5-1.5=+1.00$. The short sale of the stock means that Bank A will be liable to pay someone either $-\Delta_0 uS_0=4$ or $-\Delta_0 dS_0=1$ at time 1.
Together with the +1.00 this leaves the bank in a position of $1-4=-3$ or $1-1=0$ at time 1. However, the bank also has that long position in the derivative, balancing the -3 or 0 position out.
In the end, then, the only thing left is the investment in the money market via Bank C. It has grown to $(1+r)1.2=1.5$ at time 1.
Thus Bank A has successfully hedged a long position in the derivative.

Actually this can be simplified: the bank just sells 0.5 shares short.
The bank thus receives 2.00 at time 0, which it places in the money market, leading to 2.50 at time 1. When the bank has to pay the value of the stock at time 1 it has to pay either 4 or 1. At the same time the bank receives 3 or 0 because of the long position in the derivative. This gives a net loss of 1 at time 1, leaving the bank with $2.50-1.00=1.50$ at the end.