Even integers have the form 2k so three consecutive even integers will be 2k,2(k+1),2(k+2)
so there sum will be
2k+2(k+1)+2(k+2)=24
simplifying
2k+2k+2+2k+4=24
adding like terms
6k+6=24
6k=18
k=3
so the three consecutive even integers are
2(3),2(3+1),2(3+2)
6,8,10