For two graphic objects side by side, use the ImageSize parameter for GraphicsRow
Manipulate[ GraphicsRow[{Show[{Plot[Sin[alpha*x], {x, -5, 5}], Plot[Cos[alpha*x], {x, -5, 5}]}], Show[{Plot[Sin[alpha*x], {x, -5, 5}], Plot[Cos[beta*x], {x, -5, 5}]}]}, ImageSize -> Full], {alpha, 1, 2}, {beta, 1, 2}]

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