X + Y = 18
X=chickens, Y=Cows
2x + 4y = 60
Let's try 8 and 10.
16 + 40=56, no, 32+20=52, no. 8&10 do not work.
Let's try 9 and 9.
18+36=54, no. 9&9 do not work.
Let's try 11 & 7.
22+28=50, no. 14+44=58, no.
Let's try 12 & 6.
24+24=48, no. 12+48=60 YES!
There are 12 cows and 6 chickens.