Manipulate[Graphics[{
EdgeForm[{AbsoluteThickness[2],Gray}],AbsoluteThickness[2],
Table[Rectangle[{x,y},{x+1,y+1}],{x,0,n,2},{y,0,m,2}]
,Table[Rectangle[{x+t Sin[Pi/2y],y},{x+t Sin[Pi/2y]+1,y+1}],{x,0,2n-1,2},{y,0,m}],

Gray,
Line[Table[{{-1,y},{2n,y}},{y,0,m}]]
},
ImageSize->{400,400}],
{{t,-1,"move"},-1,1},
{{n,7,"width"},2,15,1},
{{m,7,"high"},2,15,1}
]

Graphics[{Rectangle[{0,0},{1,1}],Blue,Rectangle[{2,1},{1,2}]}]

Graphics[
Table[Rectangle[{x,y},{1,1}],{x,0,10,5},{y,0,10,2}]



]

Rectangle[{t+1,y+1},{t+2,y+2}],{x,0,n,2},{y,0,m-1,2}