Which enzyme(s) will produce a dna fragment that contains the entire vgp gene (shown in red) and has “sticky ends”?

HindIII and BamHI are the enzymes that will create a DNA fragment that carries the entire vgp gene (shown in red) and has "sticky ends"

Cloning the vgp gene requires an enzyme that has restriction sites on both sides of that gene but not within the gene.  Satisfying that requirement are the two enzymes, namely HindIII and BamHI, while at the same time, creates DNA fragments that contain sticky ends. Sticky ends make it possible for the fragments to combine with the DNA of a cloning vector, such as a plasmid

BamH I, on the other hand is a type II restriction endonuclease, having the capacity for recognizing short sequences (6 b.p.) of DNA and specifically cleaving them at a target site.