Answer
20 cables
Work Step by Step
Let us take 4 computers out of 8 , they must have at least 4 cables to access all the 4 printers. The remaining 4 computers must have 4 cables each, attached to all the printers , so that no matter the choice of 4 computers we can access the 4 printers .
Hence total cables = 4 + 4$\times$4 = 20