Sixteen 8th notes would normally make two bars of 4/4 which is why I presented that as an option too. Even though 16/8 is a silly time signature, it indicates that there are four more 8th notes than the other bars.
12/8 is not the same as 6/4 in the same way that fractions would be in math. I’ll try to come back and explain when I have more time.
In music, the magic equation to transform simple signatures into compound is to multiply and/or divide time signatures by 3/2. Keeping ‘why’ aside for a second, the time signature twins you’re looking for, are:
2/4, simple time signature - as compound, it becomes 2/4*3/2 = 6/8
Following the same thought process:
3/4 = 9/8
4/4 = 12/8
6/4 as compound would be 18/8
Compound time signatures are broken down into three-part rhythms.
The reason 16/8 equals 4/4 in the given situation is because both are SIMPLE time signatures, that means that they both can be broken down in a two-part rhythm. The first cue you should note is how the 8th notes are grouped together. 4/4 and 16/8 are basically the same visually speaking, the only difference would be how you count them: instead of 1-and-2-and-and-4-and, you would count 1, 2, 3, 4, 5… 16! in the 16/8 situation. That means 16/8 is overkill and unecessary, but just a reminder of what is possible. 16/8 is the literal description of how many 8th notes are in two measures of 4/4.