What is the correct numbering & order for this molecule?
The parent hydrocarbon chain for this molecule will be the 7 membered ring.

2.There are no functional groups with suffixes.
3.A halogen substituent(Bromine) and two side chains are present. ( methyl and t-butyl or (1,1-dimethylethyl) )
Having identified all these we can proceed to numbering the parent hydrocarbon chain.
After numbering the Parent hydrocarbon chain in all possible ways(ideally) we choose that numbering that satisfies the following criteria:
Numbering of the chain. This is done by first numbering the chain in both directions (left to right and right to left), and then choosing the numbering which follows these rules, in order of precedence.
1.Has the lowest-numbered locant (or locants) for the suffix functional group. Locants are the numbers on the carbons to which the substituent is directly attached.
2.Has the lowest-numbered locants for multiple bonds (The locant of a multiple bond is the number of the adjacent carbon with a lower number).
3.Has the lowest-numbered locants for prefixes.
In the above molecule since there are no suffix functional groups or multiple bonds we can apply criterion 3.
After numbering the parent chain all possible sets of locants are written down in the ascending order.(in this case)
eg: If the set of locants are (2,4,3) and (1,4,3) we write them as (2,3,4) and (1,3,4)
Then choose the one with the lowest possible locants. First compare the first locant, choose the ones with the lowest locant, among these sets of locants compare the second locant, choose the ones with the lowest locant and so on...
eg: If the sets of locants are (1,3,8) and (1,4,5) we choose (1,3,8)
It is only when we get two different numbering for the same compound following all the above mentioned rules that we should choose the set of locants which assign the lowest locant to the substituent or side chain on the basis of alphabetical precedence.