Draw the skeletal structure for 3,3-dimethylheptane.

The parent chain is heptane, which means 7 carbon atoms in a straight chain with only single bonds. There are two methyl groups ($-\text{CH}_3$) attached to the third carbon atom.

Skeletal structure:

      CH3
      |
CH3-CH2-C-CH2-CH2-CH2-CH3
      |
      CH3

Or, more concisely:

C-C-C(CH3)2-C-C-C-C

Which can be drawn as:

    CH3
    |
C-C-C-C-C-C-C
    |
    CH3

Or, as a skeletal line structure:

  /\
 /  \
C----C----C----C----C
|    |
CH3  CH3

Let's draw it as a clear skeletal structure:

      CH3
      |
C-C-C-C-C-C-C
      |
      CH3

This is equivalent to:

    CH3
    |
C-C-C-C-C-C-C
    |
    CH3

The skeletal structure is:

      CH3
      |
CH3-CH2-C-CH2-CH2-CH2-CH3
      |
      CH3

Which is:

    CH3
    |
C-C-C-C-C-C-C
    |
    CH3

Let's use a standard skeletal representation.

(Note: I cannot actually draw images. I will represent the skeletal structure using text-based drawing or describe it clearly.)

The skeletal structure for 3,3-dimethyl heptane is a 7-carbon chain with two branches (methyl groups) on the third carbon.

      CH3
      |
CH3-CH2-C-CH2-CH2-CH2-CH3
      |
      CH3

This can be represented as:

    CH3
    |
C-C-C-C-C-C-C
    |
    CH3

Where each vertex and end represents a carbon atom, and hydrogens are implied.

The parent chain is nonane, meaning 9 carbon atoms in a straight chain with only single bonds. There is an ethyl group ($-\text{CH}_2\text{CH}_3$) at the third carbon, and two methyl groups ($-\text{CH}_3$) at the third and fourth carbon atoms.

Skeletal structure:

          CH3
          |
CH3-CH2-C-CH-CH2-CH2-CH2-CH2-CH3
        | |
        CH3 CH2CH3

This can be represented as:

        CH3
        |
C-C-C---C-C-C-C-C-C
      | |
      CH3 CH2CH3

Let's draw it clearly:

(Again, using text-based representation for the skeletal structure.)

        CH3
        |
C-C-C---C-C-C-C-C-C
      | |
      CH3 CH2CH3

The skeletal structure for 3-ethyl-3,4-dimethylnonane is a 9-carbon chain with an ethyl group and a methyl group on the third carbon, and another methyl group on the fourth carbon.

The parent chain is hexane, meaning 6 carbon atoms.

• At carbon 1: an ethyl group ($-\text{CH}_2\text{CH}_3$) and a methyl group ($-\text{CH}_3$).
• At carbon 2: a methyl group ($-\text{CH}_3$).

Let's draw the implied structure:

Note: The name "1-ethyl-1,2-dimethyl hexane" is not a correct IUPAC name because the longest carbon chain is actually 7 carbons long (heptane), and the substituents would be at different positions. If we follow the given name strictly, the structure would be:

      CH3
      |
CH3-CH2-C-CH-CH2-CH2-CH3
      | |
      CH3 CH2CH3

However, if we identify the longest chain in this structure, it is a 7-carbon chain (heptane). Numbering from the end that gives the lowest numbers to substituents, the correct IUPAC name for this structure would be 2,3-dimethyl-2-ethylheptane, or more correctly, 2,3,3-trimethylheptane.

Given the instruction to draw the structure of the compound, I will draw the structure as implied by the name, acknowledging the naming issue.
The skeletal structure for 1-ethyl-1,2-dimethyl hexane (as named) is:

      CH3
      |
C(CH3)(CH2CH3)-CH(CH3)-C-C-C-C

This can be drawn as:

(Using text-based representation.)

      CH3
      |
C(CH3)(CH2CH3)-CH(CH3)-C-C-C-C

The structure implied by the name "1-ethyl-1,2-dimethyl hexane" is a 6-carbon chain where the first carbon has both a methyl and an ethyl group, and the second carbon has a methyl group.

The parent structure is cyclohexene, which is a 6-membered carbon ring with one double bond. The double bond is between carbon 1 and carbon 2.

• At carbon 3: a bromine atom ($\text{Br}$).
• At carbon 6: a chlorine atom ($\text{Cl}$).

We number the carbons of the double bond as C1 and C2. Then we number around the ring to give the lowest possible numbers to the substituents.
If the double bond is C1=C2, then C3 is adjacent to C2.

(Using text-based representation.)

      Cl
      |
    C---C
   /     \
  C       C=C
   \     /
    C---C
      |
      Br

Let's draw it more clearly as a skeletal structure:

The skeletal structure for 3-bromo-6-chlorocyclohex-1-ene is a 6-membered ring with a double bond. If the double bond is between C1 and C2, then a bromine atom is on C3 and a chlorine atom is on C6.