The sum of digits of a 3 digit number is 12. three times the hundreds digit minus twice the tens digit is 5. if six time the units digit is added to four times the tens digit, the result is 50. find the number.

So
xyz

x+y+z=12
3x-2y=5
6z+4y=50
so multiply 3x-2y=5 by 2
6x-4y=10
add to 6z+4y=50 and get
6x+6z+4y-4y=10+50
6x+6z=60
distribute
6(x+z)=6(10)
divide both sides by 6
x+z=10
subsitute 10 for x+z in the first equation
10+y=12
y=2
subsitute
3x-2(2)=5
3x-4=5
3x=9
x=3

x+z=10
3+z=10
z=7

x=3
y=2
z=7

number is
327