Step 1: Understanding the Question:
"Would" changes its sense depending on the sentence it sits in. We have to match each of the four listed senses, willingness, obstinacy/persistence, determination, and improbable or real condition, to the sentence that actually demonstrates it.
Step 2: Key Approach:
Take each usage sentence one at a time and ask what job "would" or "wouldn't" is doing in it, then line it up with the meaning from the list that fits that job exactly.
Step 3: Detailed Explanation:
Sentence 6, "He would do as you say", shows the subject agreeing or being ready to comply, which is a textbook case of willingness. So meaning 1 matches usage 6.
Sentence 7, "He beat the ox, but it wouldn't move", uses "wouldn't" to show the ox refusing to budge no matter what was done to it. This stubborn refusal despite effort is exactly obstinacy or persistence in refusing. So meaning 2 matches usage 7.
Sentence 5, "He would go for a walk even when it was raining", describes a repeated, habitual action carried out regardless of a real obstacle, the rain. This steady, repeated choice to act despite difficulty is what "determination" describes here. So meaning 3 matches usage 5.
Sentence 8, "If you came across a snake, what would you do?", is a classic conditional sentence, asking what someone would do under a hypothetical circumstance. So meaning 4 matches usage 8.
Putting these together gives 1-6, 2-7, 3-5, 4-8.
Step 4: Final Answer:
The correct match is 1-6, 2-7, 3-5, 4-8, which is option 2.
\[ \boxed{\text{1-6, 2-7, 3-5, 4-8}} \]