Let

$x$ = hundreds digit

$y$ = tens digit

$z$ = units digit

$100x + 10y + z$ = the number

The hundreds digit is twice the units digit

$x = 2z$ → equation (1)

The sum of the digits is 17

$x + y + z = 17$ → equation (2)

396 be subtracted from the number

$(100x + 10y + z) - 396 = 100z + 10y + x$

$99x - 99z = 396$

$x - z = 4$ → equation (3)

Substitute x = 2z to equation (3)

$2z - z = 4$

$z = 4$

From equation (1)

$x = 2(4)$

$x = 8$

From equation (2)

$8 + y + 4 = 17$

$y = 5$

The number is

$100x + 10y + z = 854$ *answer*