I am sorry I came to your question too late I think. By now it will be too late to try this. But making him vomit might be right(if you had called the vet and the vet said that was okay to do)
To make a dog vomit use 3% Hydrogen Peroxide Give your dog one teaspoon hydrogen peroxide per 10 pounds (4.5 kg) of body weight.
There is clear information here about what to do to make a dog vomit -and when to NOT do it:
Always take the dog to the vet after it has thrown up, just to be sure all is well and get it checked over.
If it was more than 2 hours since a dog ate something it shouldn't, then it is too late to induce vomiting. Vet's advice needed. And with a thing like a long strand of twine, it's important to do that quickly. Don't wait and see if the dog passes it naturally. It could get twisted up in the intestine and cause blockage or lack of circulation.
I hope your dog is okay now...?