My Dynamark riding mower will not start unless I use jumper cables. Checked battery and it pulls 12 volts checked cable going to solenoid from battery and it showed 12 volts.

The cable going from the solenoid to the starter would not test out at 12 volts. It would not test anything.

But if the solenoid is bad how can I jump start the engine using jumper cables at the battery?

This is where I get confused?

Take the battery out and get it load tested. Sometimes it's waived if you buy a battery.

Voltage tells you if you have a bad battery, but it can't tell you if it's a good battery. You can have a battery that measures 12 volts and is bad.

A load test measures the effective series resistance which is an indicator of battery health.

You can also check the terminal connections to the battery to see if they are mechanically sound.

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I did have a load test done on the battery today. It tested out fine.
I changed out two cables and on a third cable, the positive going from
The battery to the solenoid, I replaced one end. Still will not
Crank.

Where do you attach the jumper cables? The positive battery post and the fround of the engine? Or The positive battery post and the negative battery post or somewhere else?

What might the possibilities be?

Too high of a resistance somewhere. (cables, starter, starter solenoid)
(Try measuring voltages across components: Like across starting solenoid, across cables (end to end), across battery while trying to start it to see if you can identify a large voltage drop.

Battery not fully charged.

The wrong battery (not enough cold cranking amps, a deep discharge (marine) battery was installed.

My Dynamark riding mower will not start unless I use jumper cables. Checked battery and it pulls 12 volts checked cable going to solenoid from battery and it showed 12 volts.

The cable going from the solenoid to the starter would not test out at 12 volts. It would not test anything.

But if the solenoid is bad how can I jump start the engine using jumper cables at the battery?

This is where I get confused?

Okay, just because you are reading 12 volts, doesn't mean you are getting the cranking amps needed. Have the battery tested on a "load tester" battery tester. Also the cable from the solenoid to the starter will not have any voltage unless the clutch/brake is depressed and the safety switches are operating properly.