The phrase "convincing way" means to present something in a manner that makes others believe or agree with what is being said or done.
Sentences with «convincing way»
You're making assertions that the assertions are correct, not a very convincing way to make a point. (religion.blogs.cnn.com)
The most convincing way of providing this information to them this is to show them how you have produced results and solved problems for past employers. (distinctiveweb.com)