The given solution:

Initial: $($q$0,1011000,$Z$0)$

After $1$: $($q$1,011000,$XZ$0)$

After $0$: $($q$1,11000,$XXZ$0)$

After $1$: $($q$1,1000,$XXZ$0)$

After $1$: $($q$1,000,$XZ$0)$

After $0$: $($q$1,00,$Z$0)$

After $0$: $($q$2,0,$Z$0)$

After $0$: $($q$2,,$Z$0)$

Final state q$2$ accepts the string $"1011000".$

How can After $1$: $($q$1,011000,$XZ$0)($the second line ID$)$

After this id $($q$1,011000,$XZ$0)$the next id is $($q$1,11000,$XXZ$0)$ and the state remains in q$1,$ how can this happen since in the PDA there exists no transition that can loop q$1$ with a $0$ input.