$$-V D_V - P_1 D_1 - P_2 D_2 = 0 \ldots (i)$$ $$V C_V + P_1 C_1 + P_2 C_2 = 0 \ldots (ii)$$

Where
$P_1, D_1,$ and $C_1$ are value, duration, and convexity of the first bond
$P_2, D_2,$ and $C_2$ are value, duration, and convexity of the second bond
$V, D_V,$ and $C_V$ are value, duration, and convexity of the positioned to be hedged.

Working with USD million, the above equations, in this case, will be as follows:

$$-20 - 6P_1 - 4P_2 = 0 \ldots (i)$$ $$120 + 50P_1 + 20P_2 = 0 \ldots (ii)$$

Solving the above equations simultaneously, we get

$$P_1 = -1 \text{ and } P_2 = -3.5$$

Therefore, for the bank to hedge against its position, it must take a short position of 1 million in bond A and a short position of 3.5 million in bond B.

Note:
We use the elimination method to solve the simultaneous equations:
First, rewrite the equations as follows:

$$-6p1 - 4p2 = 20 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots eq\ 1$$ $$50p1 + 20p2 = -120 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots eq\ 2$$