The shared hosting provider can do that. They need to add new dns zones for the subdomains you want to have.
Before that, make sure you don't already have the subdomains created. Existing subdomains can't be redirected (well, they can but that's not the point here).
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Yes, it is possible. You just need to point your subdomains from the DNS server of your main domain (i.e. green.com). For example, d1.green.com is hosted on 220.127.116.11 and d2.green.com is on 18.104.22.168 then you will need to add following records in DNS zone: