since the man alternatively throws a coin and than tossess a coin where coin is tossed first..
so the sequence becomes = H,(5/6) + T,(1,2,3,4),H,(5,6) + T,(1,2,3,4) ,T,(1,2,3,4) ,H,(5,6)..................
=1/2 * 2/6 + 1/2*4/6 *1/2*2/6+................
=1/6 + 1/3 *1/6 +1/3*1/3*1/6+.......
=1/6( 1/(1-1/3) )= 1/4 ANSWER