The correct answer is: approached.
The word “approached” means “to come near to or to deal with in a particular way.” In this context, it means that the problems suggested by style as a sign and index of personality can be considered from many different perspectives.
The word “encountered” means “to meet or experience something unexpectedly or in a hostile way.” In this context, it would imply that the problems suggested by style as a sign and index of personality are something to be avoided or feared.
The word “confronted” means “to meet or face something difficult or dangerous.” In this context, it would imply that the problems suggested by style as a sign and index of personality are something to be overcome or defeated.
The word “upheld” means “to maintain or support something.” In this context, it would imply that the problems suggested by style as a sign and index of personality are something to be accepted or tolerated.
Therefore, the best answer is “approached,” as it allows for the most open-ended and comprehensive consideration of the problems suggested by style as a sign and index of personality.