Assumption: Values just need to exist, not that they need to be of equivalent row.
=If(IfError(Match(A2,P:P,0),0)*IfError(Match(G2,M:M,0),0)*IfError(Match(H2,L:L,0),0)>0,1,0)
For each IfError, you will output a row number (>0) if you match, or if there is no match a zero will be output. Multiply anything by zero and you get zero, whcih allows a 1 or 0 output for true/false in the overarching If-statement.
If they need to be of the same row, you can compare 2 matches, which rely on the transitive property (A=B, B=C, so A=C):
=If(And(Match(A2,P:P,0)=Match(G2,M:M,0),Match(G2,M:M,0)=Match(H2,L:L,0)),1,0)
Edit1:
Per my comment (to this answer) about false negatives, a UDF or subroutine in VBA would be more appropriate, considering Match() returns the first row that has a match.
As this is not a VBA tagged post, this is a bit above the expected answer... My recommendation would be to:
A) Ensure you are comfortable using VBA.
B) Make a post about creating a user-defined function (note that any post on here about VBA has an expectation that the poster can interact with an expert on the topic and will be putting forth effort to write the code themselves, as StackOverflow is not a code-for-you service).
To help give a lead on what may be in your UDF:
A loop to go through the values from first row to last row in the search column (i.e., L, M, & P)
A variable to dynamically identify the last row of your search column
An if-statement to compare values from your lookup values (i.e., A2, G2, H2) to the search values at the current iteration of the loop
An output of 1 (has match) or 0 (no match).
There are many ways to go about this with VBA; hopefully that's a good start for you, Irina!