Engaging the Core in Freestyle

1) Have an intention to use your hands to "hold your place" in the water, rather than to push it back. Your hand will still move back; indeed to an extent it will still push water back. But that intention will cause you to engage core muscle more and arm muscle less.

2) Using the slight leverage offered by that gripping hand/arm, drive the "high side" of your body down. This taps the free energy available from gravity to assist in your intention. It also results in your swimming with your body, rather than using your arms to drag it through the water.

In freestyle, as your left hand is "patiently" establishing a grip, the right hip will be higher than the left. Rather than exert left-arm muscles to push water back, use them to stabilize your hold on the water as you drive the right hip down. Indeed think of using your right hip to drive your right hand past the gripping left. This should result in a sensation of sending energy forward rather than back.