Final answer:
When the stock price increases and the delta of a call option increases, an investor should sell a portion of the call option to rebalance a delta-neutral hedge.
Step-by-step explanation:
In the context of delta change and rebalancing, if the stock price increases by $2 and the delta of the call option increases to 0.6, the appropriate action for an investor to rebalance the hedge would typically be to sell a portion of the call option. This is because the increased delta indicates the option's value is now more sensitive to changes in the stock price. To maintain a delta-neutral position, an investor would sell some of the call options to balance the increased delta. The investor should not exercise the call option unless it's beneficial independent of the hedging strategy.