Hello!

Let's take a look at each option, and what makes each one correct/incorrect:

To travel to China and Japan have always been John's dream.

(a) To travel to China and Japan have always
"To travel to" isn't the best way to write about actions John is dreaming of. Instead, use a gerund (a word that ends with -ing) to clearly show action. It also uses "have always," which is a plural verb - and since the topic is focused on traveling to BOTH places eventually, it makes more sense to use the singular "has always."

(b) Traveling to China and Japan has always
This one is correct because it starts with a gerund that clearly shows action, and fixed the have/has problem in A.

(c) To travel to China and Japan has
Again, "To travel to" isn't the best way to write about actions. This one also got rid of the word "always," which is important to the meaning of the sentence! He hasn't just started dreaming about it - he's been dreaming about it his whole life!

(d) To travel to China or Japan has always
This one is sneaky - they switched "China and Japan" with "China or Japan," which is different! He wants to go to both - not one or the other!

(e) Traveling to China and Japan have always
This one is wrong because it didn't fix the have/has problem from option A.

I hope this helps! I'm available if you'd like any follow up.