Ensure there is fuel in your Walker mower's gas tank before continuing. Add fuel as necessary and attempt to run your mower again.
Open the front engine cover of your Walker mower and locate the battery, which will have a distinct red wire and a distinct black wire coming out of either of its sides. These are the positive wire and the negative wire, respectively. If either of these wires are loose from the battery, reconnect them to the battery's bolts using a socket wrench.
Locate the solenoid if the battery is not the issue. The solenoid is between the Walker mower's battery and engine, and the battery's red positive wire should connect to a bolt on the solenoid's side. If it has come loose, reattach it to the side of the solenoid and tighten it in place by using your socket wrench to turn the solenoid's bolt clockwise.
Ensure the main wire connecting to the bolt on the other side of the Walker mower's solenoid is also in place. Reconnect it if necessary using your socket wrench as you did with the previous wire.
Check the wire harness. The wire harness is a "net" of smaller wires that is attached over the solenoid. Ensure the wires are making contact with the metal electrical conductors on the solenoid. Reposition the harness if they are not. You will need to disengage the wire harness retainer clip by prying under the clip with a knife and pushing it upward to release it.
Press down on the Walker mower solenoid's retainer clip to latch it back into place once you have repositioned the wire harness. Close the mower's engine cover.