Using conservation of momentum, we have:

\(6 \times 4 = 3m + 4 \times 1.5\) or \(6 \times 4 = 3m - 4 \times 1.5\)

Solving these equations gives \(m = 6\) and \(m = 10\).

Calculate the initial kinetic energy of sphere A:

\(\text{KE}_{A, \text{initial}} = \frac{1}{2} \times 4 \times 6^2 = 72 \text{ J}\)

Calculate the kinetic energy of sphere A after the collision:

\(\text{KE}_{A, \text{after}} = \frac{1}{2} \times 4 \times 1.5^2 = 4.5 \text{ J}\)

Calculate the kinetic energy of sphere B after the collision for each mass:

For \(m = 6\):

\(\text{KE}_{B, \text{after}} = \frac{1}{2} \times 6 \times 3^2 = 27 \text{ J}\)

For \(m = 10\):

\(\text{KE}_{B, \text{after}} = \frac{1}{2} \times 10 \times 3^2 = 45 \text{ J}\)

Calculate the loss of kinetic energy:

For \(m = 6\):

\(\text{KE}_{\text{loss}} = [\frac{1}{2} \times 4 \times 6^2 - \frac{1}{2} \times 4 \times 1.5^2 - \frac{1}{2} \times 6 \times 3^2] = 40.5 \text{ J}\)

For \(m = 10\):

\(\text{KE}_{\text{loss}} = [\frac{1}{2} \times 4 \times 6^2 - \frac{1}{2} \times 4 \times 1.5^2 - \frac{1}{2} \times 10 \times 3^2] = 22.5 \text{ J}\)