Is 2.58, 2.6,2 5/8,2 2/3 in order from least to greatest

Yes it is.

2.58, 2.6, 2 5/8 can be converted into 2.625, and 2 2/3 can be converted into 2.66 repeating. 

2.58, 2.6, 2.625, 2.66 for a recap.

I would first turn them all into decimals
2.58, 2.6, 2.625, 2.666
How I turned 2 5/8 and 2 2/3 into decimals: divide numerator by denominator to get the decimal. Then keep the whole number.
5/8= .625
2/3= .666

Answer is 2.58, 2.6, 2 5/8, 2 2/3

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