Number Approximation: Finding the Closest Value to 12,346

To solve the problem, we need to understand rounding principles, particularly rounding a number to the nearest ten or hundred, as implied by the given options.

Let's follow these steps:

• Step 1: Determine rounding to the nearest ten.
  If we consider $12,346$, look at the units digit (6). Since 6 is greater than or equal to 5, we round the number up to $12,350$.
• Step 2: Examine the rounding to the nearest hundred for completeness.
  The tens digit of $12,346$ is 4. Since 4 is less than 5, we would round down to $12,300$.
• Step 3: Compare the results to the choices given:
  The possible answers include $12,340$, $12,350$, $12,400$, and $12,300$. Based on our calculations, $12,350$ is correct for rounding to the nearest ten.

Thus, rounding $12,346$ to the nearest ten results in $12,350$.

Therefore, the correct answer is $\text{choice 3: } 12,350$.