The 8 courses in yellow are required for the Honors program. You must choose 2 of the 3 blue courses, and 3 of the 6 pink courses. STAT 377 is a ghost of a former course, while STAT 252 and STAT 353 are not requirements per se, but are prerequisites to STAT 441 and STAT 454, respectively.
Various other prerequisites and program requirements are not listed here; this diagram is exclusively about statistics courses.
Please check the University calendar or talk to an Honors advisor for more detailed help.