First of all, there's no need to add an extra input "selectedcountries2", you can submit your values straight from the multiselect, as it is bound to "value" with the v-model attribute.
Also, you've imported multiselect locally (in the component you've pasted), but right after that you import it globally. For starters, I suggest you remove the global import, as it makes little sense in this context.
Then, can you tell us exactly what goes wrong? Do you have the vue devtools extension in your browser which allows you to see the values assigned to your properties? Is the console showing any errors?
Is the multi-select working at all? Which library are you using exactly, and have you followed the instructions?