I'm sorry if the picture isn't clear. It is in 4/4 time and the two notes with downward facing stems (which I assume are a separate voice) are dotted quarter notes.
Edit: Attempt to clear the picture up - I left the original for reference.
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The F and D notes really ought to have two tails - up and down, as it appears (to me) that although they're written just in the tenor part, they belong in the bass. Either that, or re-write the tenor notes (F and D an octave higher) as dotted crotchets (quarter notes), and the lower F and D with down stems. But as far as playing, the order of notes is clear.
As Tim answered, the stem directions are likely incorrect.
For how to play it -- on which beat to play which note head -- see how the note heads align with those in other staves. This looks like the left hand part of a piano piece. Align it with the right hand. Look for similar patterns in other bars.