It's not clear what you're trying to do.

You say that the messagebox comes out with the first bit of code but, in fact, it won't show if FirstBandColour == Random1 and SecondBandColour != Random2 OR if FirstBandColour != Random1 and SecondBandColour == Random2.

There are even more occasions with the second bit of code when the messagebox won't show.

If you want the messagebox to always show then just use 'else' rather than 'else if'.

Suppose 'condition' is a bool expression which is either true or false, then:

if (condition)
{
   // do something
}
else
{
   // do something else
}

if (condition)
{
   // do something
}
else if (!condition)
{
   // do something else
}

if (condition)
{
   // do something
}
else if (condition2)
{
   // do something else
}

Just to add to the conversation, for your situation, it would be enough to just use if/else blocks. But to answer why your original code wasn't working, the logic was wrong. Neither condition was true so none of the message boxes would show.

Look up De Morgan's Laws and Negation of a conjunction. Put simply, to negate your first condition (the opposite of correct), you need to use the opposite operation on all operations. i.e., to negate "a == b && c == d" -> "a != b || c != d". The correct logic would be:

if(FirstBandColour == Random1 && SecondBandColour == Random2 )
{
    MessageBox.Show ("CORRECT");
}
else if(FirstBandColour != Random1 || SecondBandColour != Random2 )
{
    MessageBox.Show ("WRONG");
}

if(FirstBandColour == Random1 && SecondBandColour == Random2 && bandmultiplyercolour == bandmultiplyer )
{
    MessageBox.Show ("CORRECT");
}
else if(FirstBandColour != Random1 || SecondBandColour != Random2 || bandmultiplayercolour != bandmultiplayer )
{
    MessageBox.Show ("WRONG");
}