The actual evapotranspiration is calculated using the formula:
\[
ET_{\text{actual}} = ET_{\text{ref}} \times K_c \times K_s,
\]
where:
- \(ET_{\text{ref}}\) is the reference crop evapotranspiration (6 mm/day),
- \(K_c\) is the crop coefficient (1.2),
- \(K_s\) is the soil coefficient (0.8).
Substituting the values:
\[
ET_{\text{actual}} = 6 \times 1.2 \times 0.8 = 5.76 \, \text{mm/day}.
\]
Thus, the actual evapotranspiration is 5.76 mm/day.
Thus, the correct answer is:
\[
\boxed{\text{(A) 5.76}}.
\]