The difference between 左右 and 大概 房子大概九十平方米。
房子九十平方米左右。
I believe, 大概，左右 both mean: roughly, approximately.
Why should/must 大概 precede and 左右 follow?
Yes, both are meant approximation, but 大概 is a gross estimation - the house is approximately 900 sf; 左右 implies a calculated estimation - the house is 900 sf plus or minus.
大概 also can be used to express perceived uncertainty - 大概不好吧. 大概快到了. It is used in both measurable and non-measurable matters/objects.
左右 is used on the measurable matters/objects, like area, volume, dollar, distance...etc.
They can be used together, 這房子的面積大概在九十平方米左右 - The house's floor area is approximately 90 square meter, plus or minus. Note, in here, 大概 can be replaced by &quot;大約&quot;, which is another term for approximation.