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One way to count the occurrences of distinct values in an array is:

1. Create an empty dictionary.
2. Loop through the array.
3. For each element in the array, check if it exists in the dictionary. If it does not, add it as a key and set the value to 1. If it does exist, increment the value by 1.
4. After looping through the entire array, print out the dictionary.

Here is an example implementation in Python:

arr = [1, 2, 3, 2, 1, 3, 4, 5, 6, 5]
counts = {}

for num in arr:
    if num in counts:
        counts[num] += 1
    else:
        counts[num] = 1

print(counts)

Output:

{1: 2, 2: 2, 3: 2, 4: 1, 5: 2, 6: 1}

This shows that the number 1 occurs twice, 2 occurs twice, 3 occurs twice, 4 occurs once, 5 occurs twice, and 6 occurs once in the array.