Answer
The minimum number of beat frequencies that can be produced is $~~4$
Work Step by Step
Suppose the difference in frequency of each pair of adjacent tuning forks is $~~\Delta f = x~Hz~~$
Then any possible pair of tuning forks will produce a beat frequency of one of the following:$~~x~Hz, 2x~Hz, 3x~Hz, 4x~Hz$
The minimum number of beat frequencies that can be produced is $~~4$
