Explain the difference between accepting H0 and failing to reject H0

The basis of making a decision in a hypothesis test is looking at the test statistic, and whether there is enough evidence to reject H0 in favor of the alternative. That is not the same as saying you accept H0 if you don't have enough evidence against it. Like in a jury trial you cannot conclude that someone is innocent; you can only conclude that they are not guilty because there is not enough evidence to say they are guilty. Whether or not H0 is actually true is a fact, and cannot be proven with sample data. The best you can do is to gather evidence and determine whether you have enough evidence to reject H0 and accept the alternative. That is the real question anyway.