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There is this sentence:
"The effect is a small one - a clock on the surface of the sun would gain only about a minute a year as compared to one on the surface of the earth."

How can that clock gain a minute a year if the gravity on the surface of the sun is around 28g and the time runs slower there? Perhaps instead of "gain" there should be "lose"? Or did I misunderstand anything?

Hello Taras.

As you point out, the gravity of the Sun is greater than the Earth's, hence the time on the Sun is slower than the time on the Earth. The clock on the Earth would indicate that "more time" passed on the Earth and that the Sun "gained" one minute, meaning that less time passed on it.

I hope this clears things up.

Not really, see this quote explaining losing/gaining time:

"Clock is running fast: It is also referred to as gaining time i.e. when a normal clock covers 60 minutes, a faster clock will cover more than 60 minutes".

I assume, Stephen Hawking had misused the word "gain" in the quoted sentence, and it should say "lose" instead.

EDIT: this resulted in mistranslation of this sentence in Ukrainian language edition of this book.