Write structures for the following compounds.(a) 3-ethyl-4-methylhexane (b) 3-ethyl-5-isobutyl-3-methylnonane(c ) 4-tert-butyl-2-methylheptane (d) 5-isopropyl-3,3,4-trimethyloctane

Here's what I get  

Explanation:

(a) 3-Ethyl-4-methylhexane

The main chain is eight carbons long, with an ethyl group at C-3 and a methyl group at C-4

(b) 3-Ethyl-5-isobutyl-3-methylnonane

The main chain is nine carbons long, with an ethyl group and a methyl group on C-3 and an isobutyl group on C-5.

Note that the name isobutyl is acceptable in general use, but the preferred IUPAC name (PIN) for the group is now (since 2013) "2-methylpropan-2-yl".

The PIN for your compound is 3-ethyl-3-methyl-5-(2-methyl propan-2-yl)nonane.

(c) 4-tert-butyl-2-methylheptane

The main chain is seven carbons long, with a tert-butyl group at C-4 and a methyl group at C-2.

For some reason, the IUPAC has retained the name tert-butyl for the group, so the name you give is the PIN.

The prefix "tert" is written in italics.

(d) 5-isopropyl-3,3,4-trimethyloctane

The main chain is eight carbon atoms long, with two methyl groups on C-3 and one on C-4, and an isopropyl group on C-5.

The PIN for an isopropyl group is now "propan-2-yl", so the IUPAC name for your compound is 3,3,4-trimethyl-5-(propan-2-yl)octane.

the positions which points up in upward carbon and down in downward carbon are axial

and vice versa holds true for equatorial positions

so the correct answer with labelled diagram will be