Can you solve this math puzzle?

To solve this math puzzle, we need to identify the pattern or rule that governs the given equations. Let's analyze the provided examples step by step:

Given Equations:

1. \( 1 + 3 = 34 \)
2. \( 5 + 2 = 27 \)
3. \( 5 + 1 = 16 \)
4. \( 3 + 5 = 58 \)

We need to find the value of \( 2 + 4 \).

Step 1: Look for a Pattern

The results on the right side of the equations do not follow standard arithmetic addition. Therefore, there must be a hidden rule or operation being applied.

#### Observations:
- The result is a two-digit number.
- The first digit of the result seems to be related to one of the numbers in the equation.
- The second digit of the result seems to be related to the other number in the equation.

Step 2: Analyze Each Equation

Let's break down each equation to see if we can identify the pattern:

1. Equation: \( 1 + 3 = 34 \)
- First digit of the result: \( 3 \) (matches the second number in the equation).
- Second digit of the result: \( 4 \) (might be related to the first number in some way).

2. Equation: \( 5 + 2 = 27 \)
- First digit of the result: \( 2 \) (matches the second number in the equation).
- Second digit of the result: \( 7 \) (might be related to the first number in some way).

3. Equation: \( 5 + 1 = 16 \)
- First digit of the result: \( 1 \) (matches the second number in the equation).
- Second digit of the result: \( 6 \) (might be related to the first number in some way).

4. Equation: \( 3 + 5 = 58 \)
- First digit of the result: \( 5 \) (matches the second number in the equation).
- Second digit of the result: \( 8 \) (might be related to the first number in some way).

Step 3: Identify the Rule

From the observations:
- The first digit of the result is always the second number in the equation.
- The second digit of the result appears to be the sum of the two numbers.

Let's verify this rule with the given equations:

1. \( 1 + 3 = 34 \)
- First digit: \( 3 \) (second number).
- Second digit: \( 1 + 3 = 4 \).

2. \( 5 + 2 = 27 \)
- First digit: \( 2 \) (second number).
- Second digit: \( 5 + 2 = 7 \).

3. \( 5 + 1 = 16 \)
- First digit: \( 1 \) (second number).
- Second digit: \( 5 + 1 = 6 \).

4. \( 3 + 5 = 58 \)
- First digit: \( 5 \) (second number).
- Second digit: \( 3 + 5 = 8 \).

The rule holds for all given equations.

Step 4: Apply the Rule to Solve \( 2 + 4 \)

Using the identified rule:
- First digit: The second number in the equation, which is \( 4 \).
- Second digit: The sum of the two numbers, \( 2 + 4 = 6 \).

Thus, the result is \( 46 \).

Final Answer:

\[
\boxed{46}
\]