Plot[Sin[x], {x, 0, 2  Pi}]

Solve[Sin[x] == x - 2, {x}]

Plot[{Sin[x], x - 2}, {x, -Pi, 2  Pi}];

FindRoot[Sin[x] == x - 2, {x, 0}]

FindRoot[Sin[x] == x - 2, {x, -1}]

FindRoot[Sin[x] == x - 2, {x, 1}]

FindRoot[Sin[x] == x - 2, {x, 1.5}]