Oh God, the flashback hurts!
I remodeled the master bathroom earlier this year, and the plumbing was...troublesome...
It looks like, in pic 2, you have a shutoff valve on a supply line like you would have for a toilet, with a toilet supply line attached, in your hand.
It looks like in pic 1, you have a compression fitting on a plastic line to a female garden hose type fitting.
The valve coming out of the wall should accept either compression fitting or the fitting you have screwed on now. They both appear to be 3/8". I *think* you could ditch the line you are holding in pic 2, unscrew the female garden hose end off the compression fitting on the plastic line, ditch it, and screw the plastic line's compression fitting directly to the valve.
If not, go to Lowe's and get a compression fitting that will.