The answers are:
BamH1 (G^GATCC), followed by BamH1 (G^GATCC)
BamH1 (G^GATCC), followed by BglII (A^GATCT)
BglII (A^GATCT), followed by BglII (A^GATCT)
Since the similar sticky ends are made by both BamH1 and BglII sites can be positioned at both ends of the synthetic gene. DNA fragments made by the same enzyme can permanently be ligated.