If $4\oplus 3=19$ and $5\oplus 2=17$, then $6\oplus 4=?$

The correct answer is 34.

To solve this logical puzzle, we need to determine the mathematical rule governing the operation symbol $\oplus$.

Let the operation be defined as $a\oplus b$.

Let's test a pattern where the result is calculated by multiplying the two numbers and then adding their sum to the product:

$a\oplus b=(a\times b)+a+b$

Let's verify this pattern with the given equations:
1. For $4\oplus 3$:
$(4\times 3)+4+3=12+4+3=19$
This matches the first given equation.

2. For $5\oplus 2$:
$(5\times 2)+5+2=10+5+2=17$
This matches the second given equation.

Now, applying the established pattern to find $6\oplus 4$:
$6\oplus 4=(6\times 4)+6+4$
$6\oplus 4=24+6+4=34$

Therefore, the value of $6\oplus 4$ is equal to 34.