Day 37 - Learning Mandarin

我喜欢吃牛肉和鸡肉。

Perfect,no mistake at all.

我的一只鸡和十狗。

I am not sure what you exactly wanna say,if you're talking about "I have one chicken and ten dogs",I would suggest the edits:

我有的一只鸡和十只狗。

I wrote down the correct sentence for your reference: 我有一只鸡和十只狗。

if you're talking about "This is my chicken and those ten dogs are mine , too.",I would suggest the edits:

我的一只鸡和十只狗。

Simply "我的" ="My" or , “我有”= I have, this may not 100% accurate, but mostly works.

By the way, do you really raise 10 dogs ? This is really odd...-:)

About my anwser writing in English , edits welcome.

Day 37 - Learning Mandarin

我喜欢吃牛肉和鸡肉。is right. 
我的一只鸡和十狗。you eat ?你吃了+food/ you raising animals?你饲养了+animals

Day 37 - Learning Mandarin

我喜欢吃牛肉和鸡肉。
我养了的一只鸡和十只狗。 ？？