I like your thinking/the way you think/your way of thinking
【Teacher: "Listen carefully: Four crows are on the fence. The farmer shoots one. How many are left?"
Little Johnny: "None."
Teacher: "Can you explain that answer?"
Little Johnny: "One is shot, the others fly away. There are none left."
Teacher: "Well, that isn't the correct answer, but I like the way you think."】

My question is if we can use"I like your thinking","I like your way of thinking" or "I like your thought" instead in this situation? I can't tell the subtle difference between these four.

Question

I like your thinking/the way you think/your way of thinking
【Teacher: "Listen carefully: Four crows are on the fence. The farmer shoots one. How many are left?"
    Little Johnny: "None."
    Teacher: "Can you explain that answer?"
    Little Johnny: "One is shot, the others fly away. There are none left."
    Teacher: "Well, that isn't the correct answer, but I like the way you think."】

My question is if we can use"I like your thinking","I like your way of thinking" or "I like your thought" instead in this situation? I can't tell the subtle difference between these four.

Answer

Yes, "I like your thought' would not work here.  Also, there is a subtle difference.  With the '-ing' verb (I like your thinking, I like your way of thinking) gives the idea/notion that the thinking that is happening is somewhat continuous e.g., there is no specific end) whereas 'I like the way you think' is a statement that is clear and definite.  There is no need to add the '-ing'.

Answer

Thank you, German vogel. Yeah, I agree with you. I should have left out "I like your thought".

Answer

I think all are interchangeable, except for "I like your thought" which doesn't sound natural and is also different in meaning (the others refer to the way of thinking, not to a particular thought).