A positive key rate '01 implies a decrease in value after a given shift relative to the initial value. Hence, a 4-year key rate '01 of 0.9290 implies that the bond position will lose $0.9290 in the event of a one basis point shock to the 4-year key rate. To avoid this situation, we must determine the amount of the 4-year bond that must be sold short of neutralizing the key rate exposure.

That is,

$$\frac{0.02025}{100} \times F(4) = 0.9290$$

which implies that,

$$F(4) = 0.9290 \times \frac{100}{0.02025} = \text{USD } 4,587.65$$

Thus, Ian Klein should short $4,587.65 face amount of the 4-year bond to neutralize the exposure to the 4-year key rate. If there's a one basis point shock to the 4-year key rate, the long position will lose $0.9290, while the short position will gain approximately $0.9290.