Final answer:
A negative VP test result, indicated by no reddish-brown color after the addition of alpha-naphthol and 40% KOH, would suggest that the enteric organism does not use the butanediol pathway. A positive Methyl Red test would further confirm the use of the mixed-acid pathway.
Step-by-step explanation:
If a certain enteric organism does not use the butanediol pathway for fermenting glucose, it may utilize the mixed-acid pathway. When performing the Voges-Proskauer (VP) test, after the addition of alpha-naphthol and 40% KOH to the culture medium, a negative VP test result would be expected for an organism not using the butanediol pathway. This negative result would be indicated by the absence of a reddish-brown color, since no acetoin, an intermediate of the butanediol pathway, would be present to react with the reagents. In contrast, a positive VP test, indicated by a red color, would suggest the presence of acetoin and the use of the butanediol pathway.
For completeness, an organism using the mixed-acid pathway for fermentation can be confirmed by performing a Methyl Red (MR) test. If the organism ferments glucose via mixed acids, adding methyl red would yield a red color, due to a lower pH indicating a positive MR test. This is in line with the production of acidic fermentation end products.