I agree with mediamatrix that it's going to be 24 boats, but I have some more information and I could not fit it all into the space below his response, so I'm just going to post it here.

There was a search conducted for Nessie in 1969 that was sponsored by the World Book Encyclopaedia, and that was a sonar scan proposed by Andrew Carroll. I do not know how many boats were used in that operation, but later, in 1987, during "operation deepscan", 24 boats were used, and it's the same method, sonar scan operation. It could be that
A) there were 24 boats in the 1969 search as well, although I doubt it, since the 1987 one was "by far the largest and most intense search" to that date, or
B) your lecture shortens the story a bit, confusing details that are not that important in the story at the moment (talking about the search sponsored by the World Book Encyclopaedia and the search with 24 boats as if they were referring to the same event, after all, they were both sonar studies). This would be my guess.

Here are the references that I found:

"Andrew Carroll's sonar study (1969)
In 1969 Andrew Carroll, field researcher for the New York Aquarium in New York City, proposed a mobile sonar scan operation at Loch Ness. The project was funded by the Griffis foundation (named for Nixon Griffis, then a director of the aquarium). "

http://en.wikipedia.org/wiki/Loch_Ness_Monster

"It was decided to go ahead with Operation Deepscan the following year. So on October the 9th 1987 started the largest sonar sweep of any fresh water loch anywhere in the world.
The boats again supplied by caley cruises met at the New Clansman Hotel. As well as the 24 boats that were to take part in the operation"

http://www.nessie.co.uk/htm/searching_for_nessie/deepscan.ht...

Also see:

"So instead they put boats all the way across the top of the lake and they called it Operation "Deepscan". And they scanned the bottom of Loch Ness. As far as anybody knows, that’s the first time there has been a sonar scan of the lake bottom. They said the bottom of the lake is wrinkled up like a raisin. Lots of places to hide. I’ve got a map from Scotland. A map of Loch Ness. There were caves going off to the side also of Loch Ness. Lots of places to hide. ***I’m sure the critter heard 24 boats coming down the lake and said, time to go someplace.***"

http://jcsm.org/Creation/Hovind/seminar_part3b.html