He is in danger.Tie this ribbon to his this hand for his safety.
Is it correct?
No, it is not grammatically correct. As used in the original poster's example, "his" and "this" are both determiners, with conflicting meanings. Zero or one determiners can be used with a noun like "hand". As probablyme suggests, adjectives can be used to describe other aspects of the noun.
I believe it is grammatical, It might not be grammatical. According to Jasper, it isn't. The sentence sounds like something a child might say. A child might not remember left from right, so would refer to it as his "this" hand. It's also possible that you are pointing to your own hand and calling it "this" hand. But it really needs more context to be understood that way.
I would recommend a different adjective, like his "right hand" or his "left hand".
I've never heard of his this hand being grammatical.
But this his hand or that my answer are "marginally" grammatical in today's English, being fully grammatical 400 years ago in early modern English–and possibly more recent than that. I wouldn't recommend it for a test of English, but you could get by with it in other contexts.
Example from The life of Benjamin Franklin (1835):
Encouraged by such good success of this his first adventure, he wrote on, and sent to the press, in the same sly way, several other pieces...
.....his this hand.
The sentence is incorrect grammatically. You can't put a determiner between a possessive determiner and a noun. Instead, you can use the following structure:
Determiner + noun + of possessive.
For example, Did you see this car of Peter's?
So you can say:
Tie this ribbon to this hand of his for his safety.
But the use of 'his right hand/left hand' is more appropriate.