Final answer:
Histone modification (b) H3 lysine 9 methylation directs the formation of heterochromatin, silencing gene expression in eukaryotic cells by condensing chromatin structure.
Step-by-step explanation:
The formation of the most common type of heterochromatin in eukaryotic cells involves histone modifications, which direct the silencing of genes. Specifically, the histone modification that directs the formation of heterochromatin is (b) H3 lysine 9 methylation (H3K9me). This methylation marks the histones in a way that leads to a more condensed chromatin state, thus making the genes transcriptionally silent. This is a part of the larger framework of epigenetic regulation where both histone modifications and DNA methylation play crucial roles in controlling gene expression by altering chromatin structure. Euchromatin, on the other hand, is less densely packed and usually contains genes that are actively being expressed.