It is a sad fact of life that no matter how treasured, how handwashed only in the nicest wool wash, or how tucked up in a drawer next to a lavender bag and a cedar wood block, eventually a hand knit sock will wear a little hole.
Actually, if you only ever did the last then it probably wouldn't wear out but I also wouldn't knit any more socks for you.
H's Mum could not be accused of such wanton disregard of the glory of fluffy knitted socks, and dons a pair every evening after her bath. The surprise is not that the socks need repair, but that more socks haven't needed darning earlier.
I've mended at least one pair before, and she has the good fortune to wear out the heel flap rather than the ball of the foot which is always the first place to go on my socks, hers are infinitely more repairable (mine get binned).
The blue socks were knitted with a short row heel so to mend them I picked up the heel half of the last round before the short rows above and below the heel, then unravelled the remnants of the heel back to those stitches giving me a 'round' of 60 stitches.
From then on it was simple, I knit a round, and then a toe. It's exactly the same as an afterthought heel.
The green and yellow monkeys had the traditional heel flap so I picked up the bottom of the heel flap, re-kit the short rows and then grafted them to the bottom of the foot. That's the crib notes version anyway, there's a more detailed explanation and some photos here.
A few spare moments and a little Downton Abbey and we have four socks, not exactly as good as new, but with a new lease of life.