West was to blame. He found himself guessing because he had no clear idea the strength of his partner’s hand.
East had shown slam interest by cue bidding below game, but that was the extent of West’s knowledge.
On the other hand, West had defined the strength of his hand and was minimum for the 3S bid.
After East bid 4C it was correct for West to cue bid 4D because he had already limited his hand and East had initiated a cue bidding sequence.
The bid that was incorrect was West’s bid of 4NT. He had already bid his hand to the full, so should have bid 4S and left it to partner (the unlimited hand) to initiate Blackwood if appropriate.
When one hand is limited and the other hand unlimited, it should be the unlimited hand that assumes “captaincy” in any Blackwood enquiry.
Blackwood is NOT a slam try. It is simply a means of avoiding a slam when missing two or more key cards.
Don’t use Blackwood if any specific response will leave you wondering what to do next.