Answer
[1] (left to right): $1^{\circ}$, $2^{\circ}$, $2^{\circ}$, and $1^{\circ}$.
[2] (carbons of the parent chain left to right): $1^{\circ}$, $3^{\circ}$, and $1^{\circ}$. The carbon of the methyl substituent is a $1^{\circ}$ carbon.
[3] (carbons of the parent chain left to right): $1^{\circ}$, $4^{\circ}$, $4^{\circ}$, and $1^{\circ}$. The carbon atoms of the methyl substituents are all $1^{\circ}$ carbons.
[4] (carbons of the hexane ring clockwise starting from the top): $2^{\circ}$, $4^{\circ}$, $3^{\circ}$, $2^{\circ}$, $2^{\circ}$, and $2^{\circ}$. The carbon atoms of the methyl substituents are all $1^{\circ}$ carbons.
Work Step by Step
Carbons attached to a single carbon are primary ($1^{\circ}$) carbons.
Carbons attached to two carbon atoms are secondary ($2^{\circ}$) carbons.
Carbons attached to three carbon atoms are tertiary ($3^{\circ}$) carbons.
Carbons attached to four carbon atoms are quaternary ($4^{\circ}$) carbons.
