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First of all you don't require that extra piece of connection in the D flip flop .

Go with steps :-

Step 1 :- formulate expression for next output at each flip flop.

Q0next = Q1

Q1next = Q2 XOR Q1

Q2next = ~Q2

Initially Q2 = 1 , Q1 = 1 and Q0 = 1.

At the next clock tick.

Q0 = 1

Q1 = 0

Q2 = 0

Then in the next clock tick :-

Q0 = 0 ; Q1 = 0 ; Q2 = 1;

Then in the next clock tick :-

Q0 = 0; Q1 = 1 ; Q2 = 0 ;

In the 4th clock tick :-

Q0 = 1; Q1 = 1 ; Q2 = 1;

Thus after 4 clock edges , Q0 = 1; Q1 = 1 ; Q2 = 1;

Go with steps :-

Step 1 :- formulate expression for next output at each flip flop.

Q0next = Q1

Q1next = Q2 XOR Q1

Q2next = ~Q2

Initially Q2 = 1 , Q1 = 1 and Q0 = 1.

At the next clock tick.

Q0 = 1

Q1 = 0

Q2 = 0

Then in the next clock tick :-

Q0 = 0 ; Q1 = 0 ; Q2 = 1;

Then in the next clock tick :-

Q0 = 0; Q1 = 1 ; Q2 = 0 ;

In the 4th clock tick :-

Q0 = 1; Q1 = 1 ; Q2 = 1;

Thus after 4 clock edges , Q0 = 1; Q1 = 1 ; Q2 = 1;

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