Why do my front tires shake

This is pretty easy. There was no problem before they were balanced. That rules out worn parts, broken tire belts, warped brake rotors, and bent wheels. What that leaves is a new wheel weight didn't clip on properly and flew off leaving that wheel out-of-balance, the wheel balancer was out of calibration, or a piece of debris is stuck between the wheel and mounting hub. This happens real often with cast wheels that are corroded; not so common with steel wheels. A piece of the corroded wheel can break off and stick to the hub when the wheel is removed. When it's reinstalled in a different orientation, that chunk holds the wheel from sitting squarely on the hub. Your mechanic can find that by rotating each wheel by hand and watching a dial indicator placed next to the edge of it.