Here from the given notes, I think this is a 6/4 time signature. But I am very confused due to the rest and the note placement. Any suggestions or directions would be appreciated.
So on following your comments and way of analyzing then is this time signature for the above piece 4/8?
It's a simple triple meter, so it would be more likely to be written as 3/2. Pay attention to the direction of the note stems, as those indicate multiple voices on the same staves.
This is a 4 voice composition, with soprano in the treble clef with upwards note stems, alto with downwards notes, tenor in the bass clef with upwards note stems, and bass at the bottom.
With that knowledge, you can pick out which rests belong to which voices, although the typesetting in this example is quite good and everything lines up well.
The excerpt is written in 6/4 (or, more probably, as pointed out by @dissemin8or, 3/2) time, but the visual complexity of the multiple voices can make things confusing to sort out.
As starting point regarding multiple voices, see Rest above a note in a piano piece
To help clarify the time signature, here are the voices all written separately.
And just for kicks, here's a colorized version.
UPDATE:
The newly added excerpt is most likely in 2/4. A composer who specifically wanted 4/8 would most likely separate every eighth note to emphasize the "4 beats per measure" aspect, rather than beaming them.
