Which of the following is an example of a competency-related difficulty that a clinician might experience?
1. a woman who has been seen regularly for outpatient treatment seeks help for her adolescent son who has just been arrested for underage drinking
2. a clinician can't seem to like one of his clients, and has begun to dread his scheduled sessions
3. a clinician who works in a hospice setting struggles with feelings of deep sadness
4. all of the above
Your question is a bit vague, but I believe you are speaking about rehabilitation clinicians: vocational, physical, substance and occupational rehabilitation clinicians. If so [if not, please clarify your question and post it again for a more useful answer], then in these contexts, "competency" refers to areas of competence that the patient experiences or undergoes. In other words, in these contexts, "competency" does not in any way refer to the clinician's competence or lack thereof or struggles with patients.
A competency area refers to areas of growth, recovery, accomplishment, and vocational goals that involve planning, identifying, seeking, developing, coping, and preventing hindrances and/or outcomes. An example of an area of competence ("[c]ompetency areas [are] applicable to clients in recovery who are concerned with vocational issues") as stated by the Center for Substance Abuse Treatment is "Identifying vocational goals." Another is "Seeking appropriate education or training." Yet another is "Coping with environmental challenges."
Thus, in reference to your question, issues of competency a clinician might face cannot involve their own emotions or personality clashes, as in options 2 and 3 ("struggles with feelings" "can't seem to like"). Therefore neither 2 nor 3 can be the correct answer. Nor can option 4 be the correct answer since 2 and 3 are eliminated.
The correct answer, through the processes of definition (i.e., of "competency") and elimination (i.e., of answers outside that definition), must be option 1. But why does the situation described in option 1 fit with patient competency? To understand this, you have to know enough about clinician responsibilities and areas of competency to separate the elements of the patient situation; this is not necessarily an easy task.
The situation is that (1) the patient's son is in trouble; (2) she seeks help for him; (3) she is distraught and worried about his trouble. Point (3) is the point at which your knowledge of responsibility and competency comes into use. The situation never claims she is distraught and worried, yet she must be or she would not have breached the parameter of her treatment sessions to ask for help. How does this realization fit the situation with areas of competency?
While the clinician cannot directly provide the help she is actually asking for since that would clearly be outside her rehabilitation treatment parameters (i.e., her son's events, not her own events), the clinician can provide help with the competency area of "Coping with medical and psychological challenges." The clinician can help her cope emotionally and psychologically with this difficult situation as part of her treatment and can reasonably make referrals (or have the reception desk offer referrals) to individuals or groups who can directly provide the specific help with her son that she asks for but that she cannot receive within her rehabilitation treatment parameters. Thus option 1 is the correct answer because a patient's emotional and psychological distress and coping skill definitely fall within rehabilitation areas of competency.