Best place to start is by assigning variables, in this case I would choose the first number = x and the second number = y. From there it is just a matter of reading the sentences like an equation.
x + 2*y = 16, which is the first number plus twice (2 times) the second number equals 16
2*x + y = 14, which is twice the first number plus the second number equals 14.
Now that we have 2 equations with two unknowns we can solve either with cancellation method or with the substitution method. I generally prefer the cancellation method as it tends to involve simpler algebra.
Start by multiplying both sides of the first equation by 2, which yields:
2*x + 4*y = 32
Then subtracting the second equation (2*x + y = 14)
which will cancel out the x variable leaving 3*y = 18. Then we divide both sides of the equation by 3 which gives us
y = 6
Now that we have one of the variables we can plug it back into either of our starting equations to find the answer to the other variable.
x + 2*6 = 16, which simplifies to x + 12 = 16, subtract 12 from both sides and we find x = 4. It is always a good idea to check your answers, so we take the other equation 2*x + y= 14 and plug in our solution
2*4+ 6= 14, which simplifies to 8 + 6 = 14 which is correct.
The other method, which I find to usually be more tedious but easier to understand mathematically is the substitution method
Start by taking one of the first equations and isolating one variable
x + 2*y = 16, subtract 2*y from both sides of the equation which gives a new equation
x = 16 - 2*y
Now we take our new value of x and plug it into our other equation
2* (16 - 2*y) + y = 14
Start by multiplying out the 2 to eliminate the parentheses
32 - 4*y + y = 14
Next combine the common variables
32 -3*y =14
Subtract 32 from both sides of the equation,
-3*y = -18
divide both sides by -3 and we find that y = 6
at this point, the process is the same as the elimination method, you substitute the value of y into either of your equations, which allows you to solve for x (which we found to be 4)
remember to double check your answers and when possible always choose the method (substitution or elimination) that you are more familiar with to help prevent mistakes