What is different between the internal design of Java and C++ that lets C++ have multiple inheritance?

It's drilled into the newbie Java programmers that Java (pre-Java 8) has no multiple class inheritance, and only multiple interface inheritance, because otherwise you run into diamond inheritance problem (Class A inherits from classes B and C, both of which implement method X. So which of those classes' implementation is used when you do a.X() call?)

Clearly, C++ successfully addressed this, since it has multiple inheritance.

What's different between the internal design of Java and C++ - (i'm guessing in the method dispatch methodology, and vaguely recall that it had to do with vtables from my long-ago computer languages class) that allows this problem to be solved in C++ but prevents in Java?

To rephrase:

What is the methodology of the language design/implementation used in C++ to avoid the ambiguity of diamond inheritance problem, and why couldn't the same methodology be used in Java?