Let O=TTHHTHTTHT
and knowing p=P[head]
$ P[O;p] = p^4(1-p)^6 $
$ P_{ML}=max(p^4(1-p)^6) $
To find the max of a function one could find the derivative of the function and set the it zero and then solve for the variable that was used in finding the derivative.
$ \frac{d}{dp}(p^4(1-p)^6) = 2p^3(p-1)^5(5p - 2) $
$ 2*p^3(p-1)^5(5p - 2) = 0, p = 2/5 $
