As we know from the resource-request algorithm, which is a variant of Banker's algorithm-
Demand < Number of processes + Number of resources
now, the demand is 3 tape drives for each of the three programs, therefore 9.
let the minimum number of tapedrives or resources be R.
So,
9 < 3 + R
$\therefore$ R > 6. So minimum number of tapedrives should be 7.