To give a concrete example for the Ishtar's answer: Four-string alignment. To compute optimal two-string alignment, you write one string along one (say, horizontal) axis of a 2D-array (a matrix!) and the other one along the other array. The array is filled with edit costs, and the optimal alignment of the two strings is the one which produces the lowest cost, associated with a path through the matrix. A common way of finding such a path is by the above mentioned dynamic programming. You can look up 'Levenshtein distance' or 'edit distance' for technical details.
The basic idea can be expanded to any number of strings. For four strings you'd need a four-dimensional array, to write each string along one of the dimensions.
In practice, however, multiple string alignment is not done this way, for at least two reasons:
Lack of flexibility: Why would you need to align exactly four strings??? In computational molecular biology, for example, you might wish to align many strings (think of DNA sequences), and their number is not known in advance, but it is seldom four. You program would be useful for a very limited class of problems.
Computational complexity, in space and time. The requirements are exponential in the number of dimensions, making the approach impractical for most real-world purposes. Besides, most of the entries in such multi-dimensional array would lie on such suboptimal paths, which are never even touched, so that storing them would be simply waste of space.
So, for all practical purposes, I believe your professor was right.
