I take it you are trying to fit a new cable inner, to the cable outer that is currently installed on your mower. The cable inner is normally a number of thin strands of high tensile steel, twisted to make them moderately robust. At the handlebar end of the cable inner, there should be a short crossways piece of brass rod. The cable inner should have been passed through a transverse hole in the piece of brass rod, and soldered in place. The piece of brass rod is then positioned in the hole circled in red:
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