[daftypatty]

In the attached image of the question, it asks to draw the 2D picture of the cyclohexanes into their 3D chair conformations. I don't get why the structures for the two cyclohexanes cannot be considered the same? I mean, the C environments all seem to be same in the 2D picture, so why can't they be considered the same?

[discodermolide]

Consider the H atoms of both chairs. Make a circle around one of them, what happens to it when the one chair transforms into the other chair form? Is it in the same place?
By the way I cannot see the image you attached.

[daftypatty]

Sorry here are the pictures

[discodermolide]

So the C atoms are not in the same environment.
have a look here: http://www.chem.wisc.edu/areas/reich/handouts/nmr-c13/cdata.htm

[daftypatty]

I don't get why they are different.

When naming cycloalkanes such as a this (specifically when numbering the carbons from 1 -6), we should start C1 on the carbon with bromine since it is alphabetically ahead of methyl in this case, shouldn't it ? So in both cases, why can't we treat Br as being part of C1 and Methyl being part of C3.

Also, would C1 always be the top right corner of the cyclohexane chair ? (like the carbon on the tip of the fold)

[discodermolide]

In one set the carbons are influenced by axial substituents, in the other by equatorial. They are in different environments in the two cases.