Use Array.prototype.filter() and Array.prototype.some()

const data = [
  {name:"a", tags:["filter1", "filter2", "filter3", "filter4"]},
  {name:"b", tags:["filter5"]},
  {name:"c", tags:["filter6"]},
  {name:"d", tags:["filter3", "filter9"]}
];

const filterByTags = (arr, tags) => arr.filter(ob => ob.tags.some(tag => tags.includes(tag)));

console.log(filterByTags(data, ["filter3", "filter4", "filter6"]));

The above will return the Objects with "name" a, c, d:

• a because of filter3 or either filter4
• (b Not. because has none of filter3 4 6)
• c because of filter6
• d because of filter3

You probably want either one of these two:

const newData = data.filter(d => tags.every(t => d.tags.includes(t)));
const newData = data.filter(d => tags.some(t => d.tags.includes(t)));