Final answer:
In an SN2 reaction of (3R,4R)-3-bromo-4-methylhexane with CH₃O⁻, the configuration at the carbon bonded to the leaving group (bromine) will invert, resulting in (3S,4R)-3-methoxy-4-methylhexane as the substitution product.
Step-by-step explanation:
The question asks for the substitution products under SN2 conditions for the reaction between (3R,4R)-3-bromo-4-methylhexane and CH₃O⁻. Under SN2 conditions, the attacking nucleophile (in this case, the methoxide ion CH₃O⁻) will approach the carbon atom that is bound to the leaving group from the opposite side, leading to an inversion of configuration at that carbon. Therefore, the resulting substitution product will have a configuration opposite to the starting material. If we consider the starting material as having (3R,4R) configuration, the product will have (3S,4R) configuration, because the methyl group at position 4 does not change its configuration.
Since the resulting product can exist as stereoisomers, we show both the original configuration and the inverted configuration at the carbon where the nucleophilic substitution occurs. The product of the reaction will be (3S,4R)-3-methoxy-4-methylhexane, which exhibits the change in stereochemistry due to the SN2 mechanism.