"Ik houd het meest van dit boek."
Translation:I like this book the most.
I think "houden van" and "het liefst" each addresses fondness, so it would be awkwardly redundant.
Moreover (and perhaps more importantly), "het liefst" in your example and "het meest" in the correct translation function as adverbs that modify or qualify the verb. To do something "het liefst" means, basically, to like most doing that thing. To do something "het meest," on the other hand, means to do that thing more than anything else.
To say "Ik houd het liefst van dit boek" is saying "I like liking this book the most" or "I most like liking this book." That is, of all the books I like, I enjoy liking this one more than I enjoy liking the others. --- because "het liefst" is modifying "houd." I suppose that's possible, but that's something for a deeper metaphysical discussion. Or maybe a Van Morrison song.