Concept: Counting distinct hydrogen environments (isomer counting)
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Step 1: Understand the problem
Monohalogenation means replacing one hydrogen atom by a halogen atom.
Different products arise only when hydrogens are chemically non-equivalent.
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Step 2: Draw structure
2,4,4-Trimethylhexane has branching which creates symmetry and non-equivalent carbon atoms.
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Step 3: Identify unique hydrogen positions
We count distinct carbon environments:
• Primary carbons (different environments)
• Secondary carbons
• Tertiary carbon
Due to symmetry, some positions are equivalent.
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Step 4: Count carefully
After eliminating equivalent positions:
\[
\text{Total unique substitution positions} = 7
\]
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Final Answer:
\[
\boxed{7}
\]