Explanation

‘Walking on eggshells’ means being extremely careful about what one says or does so as not to offend or upset someone — as if walking on fragile eggshells. Option (b) (‘walking with great care’) captures only the literal image, while the idiom’s established figurative sense is about avoiding offence. Options (c) and (d) are unrelated to the idiom. Hence ‘Careful not to offend or upset others’ is the most appropriate meaning.