# Do not understand 'The gain (loss) on the stock position would then tend to offset the loss (gain) on the option position' [closed]

Currently, I am reading John Hull's Options, Futures and Other Derivatives. On page 401, the author mentions the following:

Suppose that the delta of a call option on a stock is $$0.6$$, stock price is $$\100$$ and the option price is $$\10$$. Imagine an investor who has sold call options to buy $$2,000$$ shares of a stock. The investor’s position could be hedged by buying $$0.6 \times 2,000 = 1,200 \text{ shares}.$$ The gain (loss) on the stock position would then tend to offset the loss (gain) on the option position.

I do not understand the bold sentence.

My thought: As stock price increases while keeping other factors unchanged, the payoff for a call option increases, as the difference between terminal stock price and strike price increases. Thus the call option value increases. However, it is contradicting the bold sentence.

Furthermore, in this case, delta is a positive number $$0.6$$. Wouldn't this mean that an increase in underlying asset price leads to an increase in option value?

Let $$C\left(S,t\right)$$ represent the price of the call option when the underlying price is S at time t. Now if S changes by h instantaneously, the call price becomes $$C\left(S+h, t\right)$$. So the change in the call option price is:
$$C\left(S+h, t\right) - C\left(S,t\right)$$
$$C\left(S+h, t\right) - C\left(S,t\right) \approx \frac{\partial C}{\partial S}h$$