Some three number expressions connected by the symbol * are transformed into three digit numbers according to a fixed pattern. For example, 7 * 4 * 3 becomes 437 and 8 * 6 * 4 becomes 648. Using the same pattern, what should be the result when 4 * 3 * 6 is transformed?

Introduction / Context:
This is another pattern recognition question with three numbers and a special symbol *. The expression is not meant to be evaluated by multiplication. Instead, the three numbers are rearranged to form a three digit number according to a specific rule. By studying the given examples, we need to infer the order in which the three numbers are written on the right hand side, and then apply that rule to the new triple 4, 3, and 6.

Given Data / Assumptions:

• 7 * 4 * 3 is transformed to 437. • 8 * 6 * 4 is transformed to 648. • We must find the transformation for 4 * 3 * 6. • The symbol * represents a pattern separator, not actual multiplication.

Concept / Approach:
We denote the triple as (a, b, c) in the order they appear on the left. By comparing the examples, we attempt to express the right hand side three digit number in terms of a, b, and c in a fixed order, such as (b, c, a) or (b, a, c). Once we find an ordering that is consistent across all examples, we use that same ordering for the new triple (4, 3, 6).

Step-by-Step Solution:
Step 1: For 7 * 4 * 3, a = 7, b = 4, c = 3. The result is 437, which corresponds to digits 4, 3, 7. Step 2: The order 4, 3, 7 can be expressed as (b, c, a). Step 3: For 8 * 6 * 4, a = 8, b = 6, c = 4. The result is 648. This corresponds to digits 6, 4, 8, which again match (b, c, a). Step 4: Thus the consistent rule is: for any triple (a, b, c), the transformed number is (b, c, a). Step 5: Now consider 4 * 3 * 6. Here a = 4, b = 3, c = 6. Step 6: According to the rule (b, c, a), we should write 3, 6, 4. Step 7: Therefore the transformed result is 364.

Verification / Alternative check:
Check again with the given examples to ensure there is no other simpler explanation. For both sample triples, using (b, c, a) perfectly reproduces the given three digit numbers, and no alternative ordering, such as (b, a, c) or (c, a, b), can match both examples simultaneously. This confirms that the rule is correctly identified and that 364 is the only valid result for 4 * 3 * 6.

Why Other Options Are Wrong:
Option 346 corresponds to (c, a, b), which does not fit either of the given examples. Option 643 corresponds to (c, b, a) and fails in reproducing the sample mappings. Option 463 corresponds to (a, c, b) and is inconsistent with the established rule. Option 436 corresponds to (a, b, c), the original order, whereas the examples clearly show a rearranged order.

Common Pitfalls:
One common mistake is to look for arithmetic operations like a + b + c or a × b × c, although the structure of the answers strongly suggests a concatenation rather than a computed product or sum. Another pitfall is to infer the wrong ordering from only one example without verifying it against the second example, which may lead to a contradiction.

Final Answer:
Applying the consistent pattern that transforms (a, b, c) into (b, c, a), the expression 4 * 3 * 6 becomes 364.