In this equation based pattern, 8 x 5 x 0 = 805 and 7 x 4 x 6 = 764. Following the same pattern, what is the value of 6 x 8 x 9 = ?

Introduction / Context:
This is a number pattern question where the usual multiplication sign "x" is not used in its arithmetic sense. Instead, the expressions 8 x 5 x 0 and 7 x 4 x 6 are mapped to three digit numbers 805 and 764. You must infer the pattern and apply it to 6 x 8 x 9 to determine the corresponding three digit value. Such questions test pattern spotting and handling of digits rather than actual multiplication.

Given Data / Assumptions:

• 8 x 5 x 0 = 805.
• 7 x 4 x 6 = 764.
• We must find 6 x 8 x 9 = ?
• The symbol "x" is treated as a separator, not the multiplication operator.

Concept / Approach:
Observe how the digits on the left relate to the digits on the right. In 8 x 5 x 0 = 805, the right side digits are 8, 0 and 5, which are exactly the first, third and second numbers in order. In 7 x 4 x 6 = 764, the right side digits are 7, 6 and 4, again the first, third and second numbers from the left. Therefore the pattern is that a x b x c is converted into the three digit number with digits a, c and b in that order.

Step-by-Step Solution:
Step 1: Check the first example: (8, 5, 0) on the left gives 8, 0, 5 on the right.Step 2: The order is first number, third number, then second number.Step 3: Check the second example: (7, 4, 6) on the left gives 7, 6, 4 on the right, again first, third and second.Step 4: Therefore, for (6, 8, 9), we must write digits in the order: first (6), third (9), second (8).Step 5: So 6 x 8 x 9 corresponds to the three digit number 698.

Verification / Alternative check:
There is no multiplication or addition that naturally produces 805 or 764 from the left hand triples, so a digit rearrangement rule is clearly intended. Because both given examples fit the "first, third, second" ordering perfectly and there is no contradictory example, applying the same arrangement to 6, 8 and 9 is the only reasonable approach. It yields 698, which matches one of the answer options exactly.

Why Other Options Are Wrong:

• 689, 968, 986 and 896 correspond to other permutations of the digits 6, 8 and 9 but do not follow the specific "first, third, second" order demonstrated by the examples.
• Choosing any of them would ignore the clear pattern of the given equalities.

Common Pitfalls:
Some candidates attempt to treat "x" as multiplication and look for numeric formulas like products or sums, which do not work here. Others notice the digits but mis identify the exact ordering. In pattern questions with small fixed examples, always check the position of each digit carefully before generalising to a new triple.

Final Answer:
According to the pattern, 6 x 8 x 9 corresponds to 698.