3 − x 3 + 2 + x 4 = 2

To solve the equation

\[ 3 - \frac{x}{3} + 2 + \frac{x}{4} = 2, \]

let's first combine like terms. We can simplify the left-hand side:

1. Combine the constant terms: \[ 3 + 2 = 5. \]

2. Now we rewrite the equation: \[ 5 - \frac{x}{3} + \frac{x}{4} = 2. \]

Next, isolate the terms containing \(x\) by moving the constant to the right: \[ -\frac{x}{3} + \frac{x}{4} = 2 - 5, \] which simplifies to: \[ -\frac{x}{3} + \frac{x}{4} = -3. \]

Now, let's find a common denominator for the terms with \(x\). The least common multiple of 3 and 4 is 12. Rewrite the fractions: \[ -\frac{x}{3} = -\frac{4x}{12}, \quad \frac{x}{4} = \frac{3x}{12}. \]

Now substitute these back into the equation: \[ -\frac{4x}{12} + \frac{3x}{12} = -3. \]

Combine the fractions: \[ \frac{-4x + 3x}{12} = -3. \] This simplifies to: \[ \frac{-x}{12} = -3. \]

Now multiply both sides by -12 to solve for \(x\): \[ x = 36. \]

Thus, the solution is: \[ \boxed{36}. \]