Answer
All six names are actually of one isomer of $C_{7}H_{16}$ i.e. 3-methylhexane. All six names represent one isomer: 3-methylhexane.
Work Step by Step
Draw every structure from the name of the isomer. Then write the IUPAC name.
a) Draw 3 C in straight chain. (prop means 3C). then place one sec-butyl group on C1 position. Now, write the IUPAC name. We find that there are 6C in straight chain and one $CH_{3}$ group is present at C3 position. So, the name is 3-methylhexane.
b) Draw 6 C in straight chain (hex means 6C). then place one methyl group on C4 position. Now, According to IUPAC rule, numbering must be done so that the substituent gets the minimum number. So, the numbering is done from left side and methyl group is actually present at C3 position. So, the name is 3-methylhexane.
c) Draw 5 C in straight chain (pent means 5C). Now, place one ethyl group on C2 position. Now, according to IUPAC rule, longest chain should be considered. If we numbering the longest chain, there are 6 C in longest straight chain and a methyl group is present as a substituent at C3 position. So, the name is 3-methylhexane.
d) Draw 4C in straight chain (but means 4C). Place one ethyl and one methyl group at C1 position. Now, according to IUPAC rule, longest chain should be considered. If we numbering the longest chain, there are 6 C in longest straight chain and a methyl group is present as a substituent at C3 position. So, the name is 3-methylhexane.
e) Draw 6 C in straight chain (hex means 6 C). place one methyl group at C3 position. We get the structure of 3-methylhexane.
f) Draw 5 C in straight chain (pent means 5). Now, place one ethyl group at C4 position. Now, according to IUPAC rule, longest chain should be considered. If we numbering the longest chain, there are 6 C in longest straight chain and a methyl group is present as a substituent at C3 position. So, the name is 3-methylhexane.
Look at the below figures where we can see the actual numbering of C atoms in straight chain according to IUPAC rule.
