Python 3, 13483 bytes
x=input();n=['met','eth','pro','but','pen','hex','hep','oct','non','dec'];n=list('_mepbPhHond').index(x[:-3][:3]x[0])+1;print;print(n,2*n+{'a':2,'e':0,'y':-2}[x[-3]])
Only accepts lower case, like the other answer.-51 bytes thanks to 79037662
Python 3, 134 bytes
x=input();n=['met','eth','pro','but','pen','hex','hep','oct','non','dec'].index(x[:-3][:3])+1;print(n,2*n+{'a':2,'e':0,'y':-2}[x[-3]])
Only accepts lower case, like the other answer.
Python 3, 83 bytes
x=input();n=list('_mepbPhHond').index(x[0]);print(n,2*n+{'a':2,'e':0,'y':-2}[x[-3]])
-51 bytes thanks to 79037662