Alright, lets give this a try

The first cut

cut the doughnut on a diagonal sideways. That is, think about a horizontal line through the doughnut, and tilt it diagonally. This should give you two pieces, half circles with overlapping ends - the more overlapped, the better.

The second cut

Cut the doughnut on the opposite diagonal, forming an "X" set horizontally along the side of the doughnut. This should give you six pieces - two large half-circles, and a wedge on the top and bottom of the cut, on each side of the doughnut. The hole in the middle of the doughnut makes the pieces six instead of four, if the X were cut from the top rather than the side.

The third cut

line up a cut vertically, from the top of the doughnut straight down. It should go from the front edge of the front "X", to the opposite side of the back edge of the back "X". This should cut every piece you already have, into two pieces - cutting a corner each off of, say, the right side of all the front-and-right three, and the left corner each off the back-and-left three.

The 12 pieces

The pieces are now, the front top and bottom wedges, and two corners cut off the inner right side of those wedges, the right side half-circle, and the middle wedge cut off the outer left side of that half circle, the back top and bottom wedges, with two corners cut off the outside back edge of those wedges, and the left side half-circle, and the middle wedge cut off the inner right side of that half-circle.

My crude drawing, to help with confusion

! [![enter image description here][1]][1] [1]: https://i.sstatic.net/GUzwp.jpg

The first cut

cut the doughnut on a diagonal sideways. That is, think about a horizontal cut through the doughnut, and tilt it diagonally. This should give you two pieces, half circles with overlapping ends – the more overlapped, the better.

The second cut

cut the doughnut on the opposite (symmetrical) diagonal, forming an "X" set horizontally along the side of the doughnut. This should give you six pieces – two large half-circles, and a wedge on the top and bottom of the cut, on each side of the doughnut. The hole in the middle of the doughnut makes the pieces six instead of four, if the X were cut from the top rather than the side.

The third cut

line up a cut vertically, from the top of the doughnut straight down, but diagonally (as viewed from above). It should go from the right side of the front "X" to the left side of the back "X". This should cut every piece you already have into two pieces – cutting a corner each off of, say, the right side of all the front-and-right three, and the left corner each off the back-and-left three.

The 12 pieces

The pieces are now, the front top and bottom wedges, and two corners cut off the inner right side of those wedges, the right side half-circle, and the middle wedge cut off the outer left side of that half circle, the back top and bottom wedges, with two corners cut off the outside back edge of those wedges, and the left side half-circle, and the middle wedge cut off the inner right side of that half-circle.

My crude drawing, to help with confusion