Let $p$ be the probability of success cases and $q$ be the probability of failure cases.
Given, $p = 0.6, q = 0.4$
The probability of $6$ successful throws out of $10$ can be given as:
$=\ ^{10}C_6p^6q^{10-6}\\=\ ^{10}C_6(0.6)^6(0.4)^4\\ =\ 210 \times 0.046656 \times 0.0256\\ =\ 0.2508$
Correct Answer: $A$