**Solution:**

To find the magnitude of the resultant displacement, we can use the Law of Cosines, which states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the magnitudes of those sides multiplied by the cosine of the included angle.

Let's consider the two displacements as vectors:

**Displacement 1:** Magnitude = 3m
**Displacement 2:** Magnitude = 4m

The angle between the two displacements is given as 120 degrees.

Now, let's calculate the magnitude of the resultant displacement using the Law of Cosines.

**Step 1: Convert the angle from degrees to radians**

The angle between the two displacements is 120 degrees. To use the Law of Cosines, we need to convert this angle from degrees to radians.

Angle in radians = Angle in degrees * (π/180)
= 120 * (π/180)
= 2π/3 radians

**Step 2: Apply the Law of Cosines**

According to the Law of Cosines, the magnitude of the resultant displacement can be calculated using the formula:

Resultant Displacement^2 = Displacement 1^2 + Displacement 2^2 - 2 * Displacement 1 * Displacement 2 * cos(angle)

Substituting the given values:

Resultant Displacement^2 = (3m)^2 + (4m)^2 - 2 * 3m * 4m * cos(2π/3)

Resultant Displacement^2 = 9m^2 + 16m^2 - 24m^2 * cos(2π/3)

**Step 3: Calculate the Magnitude of the Resultant Displacement**

Using the trigonometric value of cos(2π/3), we can simplify the equation further:

cos(2π/3) = -1/2

Resultant Displacement^2 = 9m^2 + 16m^2 - 24m^2 * (-1/2)
= 9m^2 + 16m^2 + 12m^2
= 37m^2

Taking the square root of both sides, we get:

Resultant Displacement = √(37m^2)
= √37 * m

Therefore, the magnitude of the resultant displacement is √37 * m.