( 1)

Y=6 is substituted into y= 12/x, and x=2 is obtained.

The straight line y=kx+4 passes through the point (2,6).

X=2 y=6 into the linear equation:

2k+4=6

k= 1

The resolution function is y=x+4.

(2)

Y=x+4 substitute y =12/X.

Pack up, take it

x？ +4x- 12=0

(x+6)(x-2)=0

X=2 or x=-6.

When x=-6, y=x+4=-6+4=-2.

Point Q coordinate (-6, -2)

Let the image of a linear function intersect the X axis at point m. Y=0 to form a linear function equation:

x+4=0 x=-4

OM=|-4|=4

S△POQ = S△MOQ+S△MOP = 4×6/2+4×|-2 |/2 = 12+4 = 16