1. Let us simplify the given vector:

$2\widehat u \times 3\widehat v = 6(\widehat u \times \widehat v)$

We are given that $\widehat u$ and $\widehat v$ are unit vectors, and the angle between them is $\theta$.

2. Use the magnitude formula for cross product:

$|\widehat u \times \widehat v| = |\widehat u|\,|\widehat v|\sin\theta$

Since both are unit vectors,

$|\widehat u|=|\widehat v|=1$

so,

$|\widehat u \times \widehat v| = \sin\theta$

Therefore,

$|2\widehat u \times 3\widehat v| = |6(\widehat u \times \widehat v)| = 6\sin\theta$

3. For $2\widehat u \times 3\widehat v$ to be a unit vector, its magnitude must be $1$:

$6\sin\theta = 1$

$\sin\theta = \frac{1}{6}$

4. Now $\theta$ is acute, so

$0 < \theta < \frac{\pi}{2}$

In the acute interval, $\sin\theta$ is strictly increasing, so the equation

$\sin\theta = \frac{1}{6}$

has exactly one solution.

5. Hence, there is exactly one value of $\theta$.

Therefore, the correct option is:

$\boxed{\text{B}}$