Final answer:
In healthcare settings, handwashing is not typically required immediately before putting gloves on, since it is assumed hands are already clean, but it is critical after removing gloves, after drawing blood, or when contamination is observed.
Step-by-step explanation:
Among the listed options, the moment that does NOT require handwashing is b) Before putting gloves on. Healthcare professionals are expected to engage in hand hygiene after removing gloves, not necessarily before donning them, although they must ensure that their hands are clean before wearing gloves. This is because hands could contaminate sterile gloves if not clean. However, the critical times for handwashing typically include after potential exposure to pathogens, such as after drawing blood from a patient (c), after removing gloves (d), or when noticing a contaminant like blood on one's hands or gloves (a).