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Solve the system by elimination method

4x+3y=0
16x+3=8y

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4x + 3y = 0
16x + 3 = 8y --> 16x - 8x = -3
Elimination depends on multiplying or dividing one of the equations to make one of the terms similar in both equations and then adds or subtracts that equation from the other equation in order to eliminate one of the unknowns.
In your problem, equation 1 we can multiply the whole equation by (4), so it will be;
16x + 12y = 0 <--- Now there is two common terms in the two equations --> (16x)

16x + 12y = 0
16x - 8y = -3
________________ subtract the two equations;
(16x - 16x) + (12y - - 8y) = (0 - - 3)
0 + (12y + 8y) = (0 + 3)
20y = 3
y = 3/20
Replace the value of (y) in any of the two main equations and you will get the value of (x)
*To check the answer, replace the values of (x) and (y) in the main two equations and see if they satisfy the equations or not.
** I also hope that you got it from me please try to solve it again by yourself and solve another similar problems and if there is anything not clear, feel free to ask me.
Good Luck

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