Final answer:
Streptococcus viridians is the organism among the given options that can cause gram-positive infective endocarditis. E. coli, Hemophilic influenzae, and Klebsiella pneumoniae are gram-negative bacteria and not commonly associated with this condition.
Step-by-step explanation:
Among the options provided, the organism that can cause gram-positive infective endocarditis is b) Streptococcus viridians. Streptococcus viridines is part of the normal flora of the mouth and can enter the bloodstream to cause endocarditis, especially if an individual has preexisting heart conditions or has undergone a procedure that breaches the normal barrier defenses, such as dental procedures. The other options listed, a) E. coli, c) Haemophilus influenzae, and d) Klebsiella pneumoniae, are gram-negative bacteria and therefore not typically associated with infective endocarditis caused by gram-positive organisms.