If I understand you correctly you just want to extract all INCOME values from ADAposentado where YEAR is "2011" and REGION is "North". If so, you're almost there!
incomeNORTH2011 <- ADAposentado$INCOME[ADAposentado$YEAR=="2011" & ADAposentado$REGION=="North"]
The ampersand ("&") is the vectorized AND operator. Do not confuse with the short-circuit AND operator "&&".
Good luck with your homework!
Steen